Question 1

Evaluate the indefinite integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

The region under the curve  ,  is rotated about the x-axis. Find the volume of the resulting solid.

Accepted Answer

A)    
B)   
C)   
D)   
E)

Question 3

Evaluate the integral using integration by parts with the indicated choices of u and dv.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Find the volume of the resulting solid if the region under the curve  from  to  is rotated about the x-axis. Round your answer to four decimal places.

Accepted Answer

The answer of Find the volume of the resulting solid...

Question 5

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 6

Use Simpson's Rule to approximate the integral with answers rounded to four decimal places.

Accepted Answer

A) 2.6098 
B) 2.9504 
C) 2.0076 
D) 2.2955

Question 7

Find the integral using an appropriate trigonometric substitution.

Accepted Answer

The answer of Find the integral using an appropriate trigonometric...

Question 8

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 9

Determine whether the integral converges or diverges. If it converges, find its value.

Accepted Answer

The answer of Determine whether the integral converges or diverges....

Question 10

Find the integral using an appropriate trigonometric substitution.

Accepted Answer

A)   
B)   
C)   
D)

Question 11

A torus is generated by rotating the circle  about the x-axis. Find the volume enclosed by the torus. Round the answer to the nearest hundredth.

Accepted Answer

The answer of A torus is generated by rotating the...

Question 12

Evaluate the integral if it is convergent.

Accepted Answer

The answer of Evaluate the integral if it is convergent....

Question 13

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 14

Eight milligrams of a dye are injected into a vein leading the an individual's heart. The concentration of dye in the aorta (in milligrams per liter) measured at 2-sec intervals is shown in the accompanying table. Use Simpson's Rule with  and the formula  to estimate the person's cardiac output, where D is the quantity of dye injected in milligrams,  is the concentration of the dye in the aorta, and R is measured in liters per minute. Round your answer to one decimal place.

Accepted Answer

The answer of Eight milligrams of a dye are injected...

Question 15

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E) None of these

Question 16

Find the integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 17

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Use the Midpoint Rule to approximate the given integral with the specified value of n. Compare your result to the actual value. Find the error in the approximation.

Accepted Answer

A)   
B)   
C) 1.00008 
D) 0.00008 
E)

Question 19

Use Simpson's Rule to approximate the integral with answers rounded to four decimal places.

Accepted Answer

A) 3.0265 
B) 2.2028 
C) 2.4774 
D) 2.7519

Question 20

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Exam 7: Techniques of Integration

Evaluate the indefinite integral.

The region under the curve , is rotated about the x-axis. Find the volume of the resulting solid.

Evaluate the integral using integration by parts with the indicated choices of u and dv.

Find the volume of the resulting solid if the region under the curve from to is rotated about the x-axis. Round your answer to four decimal places.

Evaluate the integral.

Use Simpson's Rule to approximate the integral with answers rounded to four decimal places.

Find the integral using an appropriate trigonometric substitution.

Evaluate the integral.

Determine whether the integral converges or diverges. If it converges, find its value.

Find the integral using an appropriate trigonometric substitution.

A torus is generated by rotating the circle about the x-axis. Find the volume enclosed by the torus. Round the answer to the nearest hundredth.

Evaluate the integral if it is convergent.

Evaluate the integral.

Evaluate the integral.

Find the integral.

Evaluate the integral.

Use the Midpoint Rule to approximate the given integral with the specified value of n. Compare your result to the actual value. Find the error in the approximation.

Use Simpson's Rule to approximate the integral with answers rounded to four decimal places.

Evaluate the integral.