Exam 6: Applications of Definite Integrals

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - $y = 8 - x ^ { 2 } , y = x ^ { 2 } , x = 0$

(Multiple Choice)

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Question 61

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = \sqrt { x } , y = 0 , x = 0 , x = 4$

(Multiple Choice)

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Question 62

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the $x$ -axis

(Multiple Choice)

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Question 63

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. - $y = 4 | x | , y = 4$

(Multiple Choice)

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Question 64

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line. -About the line $y = 1$

(Multiple Choice)

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Question 65

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. - $y = 2 x , \quad y = 0 , \quad x = 3$ ; revolve about the line $x = - 4$

(Multiple Choice)

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Question 66

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the $y$ -axis

(Multiple Choice)

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Question 67

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by $x = \frac { y ^ { 2 } } { 5 } , x = 0 , y = - 5 , y = 5$

(Multiple Choice)

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Question 68

A right circular cylinder is obtained by revolving the region enclosed by the line $x = r$ , the $x$ -axis, and the line $y = h$ , about the $y$ -axis. Find the volume of the cylinder.

(Multiple Choice)

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Question 69

Find the volume of the solid generated by revolving the region about the given line. -The region in the first quadrant bounded above by the line $y = 6$ , below by the line $y = \frac { 6 x } { 5 }$ , and on the left by the $y$ -axis, about the line $y = 6$

(Multiple Choice)

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Question 70

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the $y$ -axis $Find the volume of the solid generated by revolving the shaded region about the given axis. -About the y -axis y = \sqrt { 3 x }$ $y = \sqrt { 3 x }$

(Multiple Choice)

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Question 71

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - $y = 4 x , y = - \frac { x } { 4 } , x = 1$

(Multiple Choice)

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Question 72

Find the volume of the solid generated by revolving the region about the given line. -The region in the first quadrant bounded above by the line $y = 5$ , below by the curve $y = \sqrt { 5 x }$ , and on the left by the $y$ -axis, about the line $y = 5$

(Multiple Choice)

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Question 73

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. - $y = 4 x , \quad y = x ^ { 2 }$ ; revolve about the $y$ -axis

(Multiple Choice)

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Question 74

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = 7 \cos ( \pi x ) , y = 7 , x = - 0.5 , x = 0.5$

(Multiple Choice)

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Question 75

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - $y = \frac { 5 } { x } , y = 0 , x = 5 , x = 7$

(Multiple Choice)

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Question 76

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = x , y = 0 , x = 1 , x = 5$

(Multiple Choice)

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Question 77

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the $x$ -axis $Find the volume of the solid generated by revolving the shaded region about the given axis. -About the x -axis y = 4 - x ^ { 2 }$ $y = 4 - x ^ { 2 }$

(Multiple Choice)

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Question 78

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the $y$ -axis $Find the volume of the solid generated by revolving the shaded region about the given axis. -About the y -axis x = 2 \tan \left( \frac { y } { 5 } \right)$ $x = 2 \tan \left( \frac { y } { 5 } \right)$

(Multiple Choice)

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Question 79

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. - $y = \sqrt { x } , y = 0 , y = x - 6$

(Multiple Choice)

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Question 80

Showing 61 - 80 of 115

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - $y = 8 - x ^ { 2 } , y = x ^ { 2 } , x = 0$

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = \sqrt { x } , y = 0 , x = 0 , x = 4$

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the $x$ -axis

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. - $y = 4 | x | , y = 4$

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line. -About the line $y = 1$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. - $y = 2 x , \quad y = 0 , \quad x = 3$ ; revolve about the line $x = - 4$

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the $y$ -axis

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by $x = \frac { y ^ { 2 } } { 5 } , x = 0 , y = - 5 , y = 5$

A right circular cylinder is obtained by revolving the region enclosed by the line $x = r$ , the $x$ -axis, and the line $y = h$ , about the $y$ -axis. Find the volume of the cylinder.

Find the volume of the solid generated by revolving the region about the given line. -The region in the first quadrant bounded above by the line $y = 6$ , below by the line $y = \frac { 6 x } { 5 }$ , and on the left by the $y$ -axis, about the line $y = 6$

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the $y$ -axis $Find the volume of the solid generated by revolving the shaded region about the given axis. -About the y -axis y = \sqrt { 3 x }$ $y = \sqrt { 3 x }$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - $y = 4 x , y = - \frac { x } { 4 } , x = 1$

Find the volume of the solid generated by revolving the region about the given line. -The region in the first quadrant bounded above by the line $y = 5$ , below by the curve $y = \sqrt { 5 x }$ , and on the left by the $y$ -axis, about the line $y = 5$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. - $y = 4 x , \quad y = x ^ { 2 }$ ; revolve about the $y$ -axis

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = 7 \cos ( \pi x ) , y = 7 , x = - 0.5 , x = 0.5$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - $y = \frac { 5 } { x } , y = 0 , x = 5 , x = 7$

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = x , y = 0 , x = 1 , x = 5$

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the $x$ -axis $Find the volume of the solid generated by revolving the shaded region about the given axis. -About the x -axis y = 4 - x ^ { 2 }$ $y = 4 - x ^ { 2 }$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. - $y = \sqrt { x } , y = 0 , y = x - 6$

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Exam 6: Applications of Definite Integrals

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - y=8−x2,y=x2,x=0y = 8 - x ^ { 2 } , y = x ^ { 2 } , x = 0y=8−x2,y=x2,x=0

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - y=x,y=0,x=0,x=4y = \sqrt { x } , y = 0 , x = 0 , x = 4y=x​,y=0,x=0,x=4

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the xxx -axis

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. - y=4∣x∣,y=4y = 4 | x | , y = 4y=4∣x∣,y=4

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line. -About the line y=1y = 1y=1

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. - y=2x,y=0,x=3y = 2 x , \quad y = 0 , \quad x = 3y=2x,y=0,x=3 ; revolve about the line x=−4x = - 4x=−4

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the yyy -axis

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x=y25,x=0,y=−5,y=5x = \frac { y ^ { 2 } } { 5 } , x = 0 , y = - 5 , y = 5x=5y2​,x=0,y=−5,y=5

A right circular cylinder is obtained by revolving the region enclosed by the line x=rx = rx=r , the xxx -axis, and the line y=hy = hy=h , about the yyy -axis. Find the volume of the cylinder.

Find the volume of the solid generated by revolving the region about the given line. -The region in the first quadrant bounded above by the line y=6y = 6y=6 , below by the line y=6x5y = \frac { 6 x } { 5 }y=56x​ , and on the left by the yyy -axis, about the line y=6y = 6y=6

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the yyy -axis y=3xy = \sqrt { 3 x }y=3x​

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - y=4x,y=−x4,x=1y = 4 x , y = - \frac { x } { 4 } , x = 1y=4x,y=−4x​,x=1

Find the volume of the solid generated by revolving the region about the given line. -The region in the first quadrant bounded above by the line y=5y = 5y=5 , below by the curve y=5xy = \sqrt { 5 x }y=5x​ , and on the left by the yyy -axis, about the line y=5y = 5y=5

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. - y=4x,y=x2y = 4 x , \quad y = x ^ { 2 }y=4x,y=x2 ; revolve about the yyy -axis

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - y=7cos⁡(πx),y=7,x=−0.5,x=0.5y = 7 \cos ( \pi x ) , y = 7 , x = - 0.5 , x = 0.5y=7cos(πx),y=7,x=−0.5,x=0.5

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - y=5x,y=0,x=5,x=7y = \frac { 5 } { x } , y = 0 , x = 5 , x = 7y=x5​,y=0,x=5,x=7

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - y=x,y=0,x=1,x=5y = x , y = 0 , x = 1 , x = 5y=x,y=0,x=1,x=5

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the xxx -axis y=4−x2y = 4 - x ^ { 2 }y=4−x2

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the yyy -axis x=2tan⁡(y5)x = 2 \tan \left( \frac { y } { 5 } \right)x=2tan(5y​)

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. - y=x,y=0,y=x−6y = \sqrt { x } , y = 0 , y = x - 6y=x​,y=0,y=x−6

Functions

Limits and Derivatives

Differentiation

Applications of Derivatives

Integration

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Filters

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - $y = 8 - x ^ { 2 } , y = x ^ { 2 } , x = 0$

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = \sqrt { x } , y = 0 , x = 0 , x = 4$

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the $x$ -axis

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. - $y = 4 | x | , y = 4$

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line. -About the line $y = 1$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. - $y = 2 x , \quad y = 0 , \quad x = 3$ ; revolve about the line $x = - 4$

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the $y$ -axis

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by $x = \frac { y ^ { 2 } } { 5 } , x = 0 , y = - 5 , y = 5$

A right circular cylinder is obtained by revolving the region enclosed by the line $x = r$ , the $x$ -axis, and the line $y = h$ , about the $y$ -axis. Find the volume of the cylinder.

Find the volume of the solid generated by revolving the region about the given line. -The region in the first quadrant bounded above by the line $y = 6$ , below by the line $y = \frac { 6 x } { 5 }$ , and on the left by the $y$ -axis, about the line $y = 6$

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the $y$ -axis $Find the volume of the solid generated by revolving the shaded region about the given axis. -About the y -axis y = \sqrt { 3 x }$ $y = \sqrt { 3 x }$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - $y = 4 x , y = - \frac { x } { 4 } , x = 1$

Find the volume of the solid generated by revolving the region about the given line. -The region in the first quadrant bounded above by the line $y = 5$ , below by the curve $y = \sqrt { 5 x }$ , and on the left by the $y$ -axis, about the line $y = 5$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. - $y = 4 x , \quad y = x ^ { 2 }$ ; revolve about the $y$ -axis

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = 7 \cos ( \pi x ) , y = 7 , x = - 0.5 , x = 0.5$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. - $y = \frac { 5 } { x } , y = 0 , x = 5 , x = 7$

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = x , y = 0 , x = 1 , x = 5$

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the $x$ -axis $Find the volume of the solid generated by revolving the shaded region about the given axis. -About the x -axis y = 4 - x ^ { 2 }$ $y = 4 - x ^ { 2 }$

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis. - $y = \sqrt { x } , y = 0 , y = x - 6$