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 x-axis. - $x = 8 y ^ { 2 } , x = 8 \sqrt [ 3 ] { y }$

(Multiple Choice)

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Question 101

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 102

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. - $y = 7 \sqrt { x } , y = 0 , x = 1$

(Multiple Choice)

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Question 103

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

(Multiple Choice)

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Question 104

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 $y = 1$ , below by the curve $y = \sqrt { \sin 2 x }$ , and on the left by the $y$ -axis, about the line $y = 1$

(Multiple Choice)

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Question 105

Find the volume of the solid generated by revolving the region about the y-axis. -The region in the first quadrant bounded on the left by the circle $x ^ { 2 } + y ^ { 2 } = 4$ , on the right by the line $x = 2$ , and above by the line $\mathrm { y } = 2$

(Multiple Choice)

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Question 106

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line. -About the line $y = 8$ $Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line. -About the line y = 8 x = 6 y - y ^ { 2 }$ $x = 6 y - y ^ { 2 }$

(Multiple Choice)

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Question 107

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = 8 x , y = 8 , x = 0$

(Multiple Choice)

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Question 108

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 109

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the $x$ -axis $Find the volume of the solid generated by revolving the shaded region about the given axis. -About the x -axis y = 9 - x ^ { 2 }$ $y = 9 - x ^ { 2 }$

(Multiple Choice)

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Question 110

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 $Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the x -axis x = y ^ { 2 } / 3$ $x = y ^ { 2 } / 3$

(Multiple Choice)

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Question 111

Find the volume of the described solid. -The solid lies between planes perpendicular to the $x$ -axis at $x = - 6$ and $x = 6$ . The cross sections perpendicular to the $x$ -axis between these planes are squares whose bases run from the semicircle $y = - \sqrt { 36 - x ^ { 2 } }$ to the semicircle $y = \sqrt { 36 - x ^ { 2 } }$ .

(Multiple Choice)

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Question 112

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = x ^ { 2 } + 3 , y = 3 x + 3$

(Multiple Choice)

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Question 113

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = - 4 x + 8 , y = 4 x , x = 0$

(Multiple Choice)

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Question 114

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. - $y = 3 x ^ { 2 } , y = 3 \sqrt { x }$

(Multiple Choice)

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Question 115

Showing 101 - 115 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 x-axis. - $x = 8 y ^ { 2 } , x = 8 \sqrt [ 3 ] { y }$

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

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. - $y = 7 \sqrt { x } , y = 0 , x = 1$

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

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 $y = 1$ , below by the curve $y = \sqrt { \sin 2 x }$ , and on the left by the $y$ -axis, about the line $y = 1$

Find the volume of the solid generated by revolving the region about the y-axis. -The region in the first quadrant bounded on the left by the circle $x ^ { 2 } + y ^ { 2 } = 4$ , on the right by the line $x = 2$ , and above by the line $\mathrm { y } = 2$

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = 8 x , y = 8 , x = 0$

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 shaded region about the given axis. -About the $x$ -axis $Find the volume of the solid generated by revolving the shaded region about the given axis. -About the x -axis y = 9 - x ^ { 2 }$ $y = 9 - x ^ { 2 }$

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = x ^ { 2 } + 3 , y = 3 x + 3$

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = - 4 x + 8 , y = 4 x , x = 0$

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. - $y = 3 x ^ { 2 } , y = 3 \sqrt { x }$

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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 x-axis. - x=8y2,x=8y3x = 8 y ^ { 2 } , x = 8 \sqrt [ 3 ] { y }x=8y2,x=83y​

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

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=7x,y=0,x=1y = 7 \sqrt { x } , y = 0 , x = 1y=7x​,y=0,x=1

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the yyy -axis x=y25x = \frac { y ^ { 2 } } { 5 }x=5y2​

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=1y = 1y=1 , below by the curve y=sin⁡2xy = \sqrt { \sin 2 x }y=sin2x​ , and on the left by the yyy -axis, about the line y=1y = 1y=1

Find the volume of the solid generated by revolving the region about the y-axis. -The region in the first quadrant bounded on the left by the circle x2+y2=4x ^ { 2 } + y ^ { 2 } = 4x2+y2=4 , on the right by the line x=2x = 2x=2 , and above by the line y=2\mathrm { y } = 2y=2

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=8y = 8y=8 x=6y−y2x = 6 y - y ^ { 2 }x=6y−y2

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - y=8x,y=8,x=0y = 8 x , y = 8 , x = 0y=8x,y=8,x=0

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 shaded region about the given axis. -About the xxx -axis y=9−x2y = 9 - x ^ { 2 }y=9−x2

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 x=y2/3x = y ^ { 2 } / 3x=y2/3

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - y=x2+3,y=3x+3y = x ^ { 2 } + 3 , y = 3 x + 3y=x2+3,y=3x+3

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - y=−4x+8,y=4x,x=0y = - 4 x + 8 , y = 4 x , x = 0y=−4x+8,y=4x,x=0

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=3x2,y=3xy = 3 x ^ { 2 } , y = 3 \sqrt { x }y=3x2,y=3x​

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 x-axis. - $x = 8 y ^ { 2 } , x = 8 \sqrt [ 3 ] { y }$

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

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. - $y = 7 \sqrt { x } , y = 0 , x = 1$

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

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 $y = 1$ , below by the curve $y = \sqrt { \sin 2 x }$ , and on the left by the $y$ -axis, about the line $y = 1$

Find the volume of the solid generated by revolving the region about the y-axis. -The region in the first quadrant bounded on the left by the circle $x ^ { 2 } + y ^ { 2 } = 4$ , on the right by the line $x = 2$ , and above by the line $\mathrm { y } = 2$

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = 8 x , y = 8 , x = 0$

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 shaded region about the given axis. -About the $x$ -axis $Find the volume of the solid generated by revolving the shaded region about the given axis. -About the x -axis y = 9 - x ^ { 2 }$ $y = 9 - x ^ { 2 }$

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = x ^ { 2 } + 3 , y = 3 x + 3$

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. - $y = - 4 x + 8 , y = 4 x , x = 0$

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. - $y = 3 x ^ { 2 } , y = 3 \sqrt { x }$