Question 1

Find the smallest n such that the error estimate in the approximation of the definite integral  is less than 0.00001 using the Trapezoidal Rule. Use a graphing utility to estimate the maximum of the absolute value of the second derivative. ​

Accepted Answer

A)  208 
B)  189 
C)  196 
D)  201 
E)  188

Question 2

Use partial fractions to find  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

Solve  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Determine whether the improper integral  diverges or converges. Evaluate the integral if it converges.

Accepted Answer

A)   
B)   
C)   
D)   
E)  diverges

Question 5

Find the indefinite integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Determine whether the improper integral  diverges or converges. Evaluate the integral if it converges. ​

Accepted Answer

A)   
B)   
C)  diverges 
D)   
E)

Question 7

Find the indefinite integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Find the area between the x-axis and the graph of the function  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 20 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​  ​

Accepted Answer

A)  The Trapezoidal rule gives 92.289382 and Simpson's rule gives 96.886125. 
B)  The Trapezoidal rule gives 92.272500 and Simpson's rule gives 92.266873. 
C)  The Trapezoidal rule gives 92.289382 and Simpson's rule gives 92.266873. 
D)  The Trapezoidal rule gives 92.272500 and Simpson's rule gives 96.886125. 
E)  The Trapezoidal rule gives -92.272500 and Simpson's rule gives -92.266873.

Question 10

Find  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Find the indefinite integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Find the indefinite integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Find the smallest n such that the error estimate in the approximation of the definite integral  is less than 0.00001 using Simpson's Rule. ​

Accepted Answer

A)  12 
B)  18 
C)  8 
D)  10 
E)  15

Question 14

Find the indefinite integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Find the smallest n such that the error estimate in the approximation of the definite integral  is less than 0.00001 using Simpson's Rule. ​

Accepted Answer

A)  65 
B)  10 
C)  13 
D)  18 
E)  23

Question 16

A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet  where the variable force required is  pounds. Find the work done in pushing the block the full 4 feet through the machine. Round your answer to three decimal places. ​

Accepted Answer

A)   ft. lbs 
B)   ft. lbs 
C)   ft. lbs 
D)   ft. lbs 
E)   ft. lbs

Question 17

Find the indefinite integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Find the indefinite integral. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Use the error formula to estimate the error in approximating the integral  with  using Simpson's Rule. Round your answer to six decimal places. ​

Accepted Answer

A)  0.003341 
B)  0.023613 
C)  0.001312 
D)  0.010495 
E)  0.031484

Question 20

Determine whether the improper integral  diverges or converges.

Accepted Answer

A)   
B)

Exam 8: Integration Techniques and Improper Integrals

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using the Trapezoidal Rule. Use a graphing utility to estimate the maximum of the absolute value of the second derivative.

Use partial fractions to find $Use partial fractions to find . A) B) C) D) E)$ .

Solve .

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Find the indefinite integral.

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Find the indefinite integral.

Find the area between the x-axis and the graph of the function .

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 20 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

Find .

Find the indefinite integral.

Find the indefinite integral.

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using Simpson's Rule.

Find the indefinite integral.

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using Simpson's Rule.

A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet where the variable force required is pounds. Find the work done in pushing the block the full 4 feet through the machine. Round your answer to three decimal places.

Find the indefinite integral.

Find the indefinite integral.

Use the error formula to estimate the error in approximating the integral with using Simpson's Rule. Round your answer to six decimal places.

Determine whether the improper integral diverges or converges.

Exam 8: Integration Techniques and Improper Integrals

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using the Trapezoidal Rule. Use a graphing utility to estimate the maximum of the absolute value of the second derivative. ​

Use partial fractions to find .

Solve .

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Find the indefinite integral.

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. ​

Find the indefinite integral.

Find the area between the x-axis and the graph of the function .

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 20 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​ ​

Find .

Find the indefinite integral.

Find the indefinite integral.

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using Simpson's Rule. ​

Find the indefinite integral.

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using Simpson's Rule. ​

A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet where the variable force required is pounds. Find the work done in pushing the block the full 4 feet through the machine. Round your answer to three decimal places. ​

Find the indefinite integral.

Find the indefinite integral. ​ ​

Use the error formula to estimate the error in approximating the integral with using Simpson's Rule. Round your answer to six decimal places. ​

Determine whether the improper integral diverges or converges.

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using the Trapezoidal Rule. Use a graphing utility to estimate the maximum of the absolute value of the second derivative.

Use partial fractions to find $Use partial fractions to find . A) B) C) D) E)$ .

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 20 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using Simpson's Rule.

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using Simpson's Rule.

A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet where the variable force required is pounds. Find the work done in pushing the block the full 4 feet through the machine. Round your answer to three decimal places.

Find the indefinite integral.

Use the error formula to estimate the error in approximating the integral with using Simpson's Rule. Round your answer to six decimal places.