Question 1

Find the area of the region enclosed by 2y = x2 and y = x + 4.

Accepted Answer

Question 2

Simplify sinh (cosh - 16).

Accepted Answer

The answer of Simplify sinh (cosh - 16)....

Question 3

Find the area of the surface generated when   from x = 3 to x = 6 is revolved about the x-axis.

Accepted Answer

The answer of Find the area of the surface generated...

Question 4

$\int$ cosh7x sinh x dx =

Accepted Answer

A)  8 cosh8x + C 
B)  cosh8x + C 
C)    
D)  7 cosh8x + C 
E)    
A)  8 cosh8x + C 
B)  cosh8x + C 
C)    
D)  7 cosh8x + C 
E)

Question 5

A constant force of 44 lb moves an object 63 ft. How much work is done in moving the object?

Accepted Answer

The answer of A constant force of 44 lb moves...

Question 6

Find the arc length of the curve y = cos x over the interval x = 0 to x = 2 $\pi$. Approximate area to four decimal places. Use a CAS if necessary.

Accepted Answer

The answer of Find the arc length of the curve...

Question 7

Find the volume of the hemisphere created by rotating the area enclosed by the circle x2 + y2 = 4 and above y = 0, around the y-axis. Approximate area to three decimal places.

Accepted Answer

A)  5.333 
B)  18.850 
C)  16.755 
D)  33.510 
E)  7.255 
A)  5.333 
B)  18.850 
C)  16.755 
D)  33.510 
E)  7.255

Question 8

Find the arc length of the curve y = x2 - 2x + 8 over the interval x = 0 to x = 3. Approximate area to three decimal places.

Accepted Answer

The answer of Find the arc length of the curve...

Question 9

Find the area of the region enclosed by y = x + 8 and y = x2 - 4.

Accepted Answer

The answer of Find the area of the region enclosed...

Question 10

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y2 = 2x and x = 8 is revolved about the line x = 11.

Accepted Answer

Question 11

Answer true or false. A 106 ft2 flat sheet of material is submerged vertically in water. The force acting on each side must be the same.

Accepted Answer

A) True 
 B)False

Question 12

Answer true or false.   = 0

Accepted Answer

A) True 
 B)False

Question 13

Use cylindrical shells to find the volume of the solid generated when the region R in the first quadrant enclosed between   , y = 0, and x = 1 is revolved about the y-axis.

Accepted Answer

The answer of Use cylindrical shells to find the volume...

Question 14

Answer true or false. The volume of the solid that results when the region enclosed by the curves   , y = 0, x = 0, x = 5 is revolved about the x-axis is given by   .

Accepted Answer

A) True 
 B)False

Question 15

Use a graphing utility to find the area of the region enclosed by the curves y = x7, y = x -5, x = 0, x = 1.

Accepted Answer

The answer of Use a graphing utility to find the...

Question 16

Use a graphing utility to find the area of the region enclosed by the curves y = x2 + 3, y = 2, x = 2, x = 4.

Accepted Answer

Question 17

Answer true or false. The arc length of the curve   from x = 5 to x = 7 is 2.084.

Accepted Answer

A) True 
 B)False

Question 18

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y2 = 4x, x = 1, and y = 0 is revolved about the y-axis.

Accepted Answer

Question 19

Use a graphing utility to find the area enclosed by the curves y = x5, y = -x2, x = 0, x = 2. Approximate area to three decimal places.

Accepted Answer

A)  13.333 
B)  8.000 
C)  8.400 
D)  4.400 
E)  2.000 
A)  13.333 
B)  8.000 
C)  8.400 
D)  4.400 
E)  2.000

Question 20

Use cylindrical shells to find the volume of the solid generated when the region R in the first quadrant enclosed between y = cos (x2) and y = 0 over the interval   is revolved about the y-axis. Approximate area to three decimal places.

Accepted Answer

Find the area of the region enclosed by 2y = x² and y = x + 4.

Simplify sinh (cosh ^- ¹6).

Find the area of the surface generated when from x = 3 to x = 6 is revolved about the x-axis.

$\int$ cosh⁷x sinh x dx =

A constant force of 44 lb moves an object 63 ft. How much work is done in moving the object?

Find the arc length of the curve y = cos x over the interval x = 0 to x = 2 $\pi$ . Approximate area to four decimal places. Use a CAS if necessary.

Find the volume of the hemisphere created by rotating the area enclosed by the circle x² + y² = 4 and above y = 0, around the y-axis. Approximate area to three decimal places.

Find the arc length of the curve y = x² - 2x + 8 over the interval x = 0 to x = 3. Approximate area to three decimal places.

Find the area of the region enclosed by y = x + 8 and y = x² - 4.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y² = 2x and x = 8 is revolved about the line x = 11.

Answer true or false. A 106 ft² flat sheet of material is submerged vertically in water. The force acting on each side must be the same.

Answer true or false. = 0

Use cylindrical shells to find the volume of the solid generated when the region R in the first quadrant enclosed between , y = 0, and x = 1 is revolved about the y-axis.

Answer true or false. The volume of the solid that results when the region enclosed by the curves , y = 0, x = 0, x = 5 is revolved about the x-axis is given by .

Use a graphing utility to find the area of the region enclosed by the curves y = x⁷, y = x -5, x = 0, x = 1.

Use a graphing utility to find the area of the region enclosed by the curves y = x² + 3, y = 2, x = 2, x = 4.

Answer true or false. The arc length of the curve from x = 5 to x = 7 is 2.084.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y² = 4x, x = 1, and y = 0 is revolved about the y-axis.

Use a graphing utility to find the area enclosed by the curves y = x⁵, y = -x², x = 0, x = 2. Approximate area to three decimal places.

Use cylindrical shells to find the volume of the solid generated when the region R in the first quadrant enclosed between y = cos (x²) and y = 0 over the interval is revolved about the y-axis. Approximate area to three decimal places.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 6: Applications of the Definite Integral in Geometry, Science and Engineering

Find the area of the region enclosed by 2y = x2 and y = x + 4.

Simplify sinh (cosh - 16).

Find the area of the surface generated when from x = 3 to x = 6 is revolved about the x-axis.

∫\int∫ cosh7x sinh x dx =

A constant force of 44 lb moves an object 63 ft. How much work is done in moving the object?

Find the arc length of the curve y = cos x over the interval x = 0 to x = 2 π\piπ . Approximate area to four decimal places. Use a CAS if necessary.

Find the volume of the hemisphere created by rotating the area enclosed by the circle x2 + y2 = 4 and above y = 0, around the y-axis. Approximate area to three decimal places.

Find the arc length of the curve y = x2 - 2x + 8 over the interval x = 0 to x = 3. Approximate area to three decimal places.

Find the area of the region enclosed by y = x + 8 and y = x2 - 4.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y2 = 2x and x = 8 is revolved about the line x = 11.

Answer true or false. A 106 ft2 flat sheet of material is submerged vertically in water. The force acting on each side must be the same.

Answer true or false. = 0

Use cylindrical shells to find the volume of the solid generated when the region R in the first quadrant enclosed between , y = 0, and x = 1 is revolved about the y-axis.

Answer true or false. The volume of the solid that results when the region enclosed by the curves , y = 0, x = 0, x = 5 is revolved about the x-axis is given by .

Use a graphing utility to find the area of the region enclosed by the curves y = x7, y = x -5, x = 0, x = 1.

Use a graphing utility to find the area of the region enclosed by the curves y = x2 + 3, y = 2, x = 2, x = 4.

Answer true or false. The arc length of the curve from x = 5 to x = 7 is 2.084.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y2 = 4x, x = 1, and y = 0 is revolved about the y-axis.

Use a graphing utility to find the area enclosed by the curves y = x5, y = -x2, x = 0, x = 2. Approximate area to three decimal places.

Use cylindrical shells to find the volume of the solid generated when the region R in the first quadrant enclosed between y = cos (x2) and y = 0 over the interval is revolved about the y-axis. Approximate area to three decimal places.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Find the area of the region enclosed by 2y = x² and y = x + 4.

Simplify sinh (cosh ^- ¹6).

$\int$ cosh⁷x sinh x dx =

Find the arc length of the curve y = cos x over the interval x = 0 to x = 2 $\pi$ . Approximate area to four decimal places. Use a CAS if necessary.

Find the volume of the hemisphere created by rotating the area enclosed by the circle x² + y² = 4 and above y = 0, around the y-axis. Approximate area to three decimal places.

Find the arc length of the curve y = x² - 2x + 8 over the interval x = 0 to x = 3. Approximate area to three decimal places.

Find the area of the region enclosed by y = x + 8 and y = x² - 4.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y² = 2x and x = 8 is revolved about the line x = 11.

Answer true or false. A 106 ft² flat sheet of material is submerged vertically in water. The force acting on each side must be the same.

Use a graphing utility to find the area of the region enclosed by the curves y = x⁷, y = x -5, x = 0, x = 1.

Use a graphing utility to find the area of the region enclosed by the curves y = x² + 3, y = 2, x = 2, x = 4.

Use cylindrical shells to find the volume of the solid that results when the region enclosed by y² = 4x, x = 1, and y = 0 is revolved about the y-axis.

Use a graphing utility to find the area enclosed by the curves y = x⁵, y = -x², x = 0, x = 2. Approximate area to three decimal places.

Use cylindrical shells to find the volume of the solid generated when the region R in the first quadrant enclosed between y = cos (x²) and y = 0 over the interval is revolved about the y-axis. Approximate area to three decimal places.