Question 1

Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule with n subintervals.

Accepted Answer

The answer of Find a bound on the error in...

Question 2

A corporation is building a complex of homes, offices, stores, schools, and churches in a rural community. As a result of this development, the planners have estimated that the community's population (in thousands) t years from now will be given by  .
What will the average population of the community be over the next 10 years?

Accepted Answer

The answer of A corporation is building a complex of...

Question 3

Find the area bounded by the curves  and  between  and  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Evaluate the integral using an appropriate trigonometric substitution.

Accepted Answer

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

Question 5

Use (a) the Trapezoidal Rule and (b) Simpson's Rule to approximate the integral to four decimal places. Compare your results with the exact value.

Accepted Answer

The answer of Use (a) the Trapezoidal Rule and (b)...

Question 6

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

Find the integral.

Accepted Answer

The answer of Find the integral. ...

Question 8

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Evaluate the integral.

Accepted Answer

A)   
B)   
C) 11.8665 
D) 6.5700 
E) 0.7166

Question 10

Use the Trapezoidal Rule to approximate the integral with answers rounded to four decimal places.

Accepted Answer

A) 0.8528 
B) 0.9842 
C) 0.4921 
D) 0.4695

Question 11

Write the form of the partial fraction decomposition of the rational expression. Do not find the numerical values of the constants.

Accepted Answer

A)   
B)   
C)   
D)

Question 12

Make a substitution to express the integrand as a rational function and then evaluate the integral.  Round the answer to four decimal places.

Accepted Answer

The answer of Make a substitution to express the integrand...

Question 13

Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule with n subintervals.

Accepted Answer

The answer of Find a bound on the error in...

Question 14

The region  is represented below. Find the area of this region to two decimal places.

Accepted Answer

A)  15.87 
B)  17.89 
C) 20.28 
D)   
E)

Question 15

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 16

A particle moves on a straight line with velocity function   . Find its position function  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Find the integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 18

Find the integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 19

Evaluate the integral.

Accepted Answer

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

Question 20

Use a table of integrals to evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)

Exam 7: Techniques of Integration

Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule with n subintervals.

Find the area bounded by the curves and between and .

Evaluate the integral using an appropriate trigonometric substitution.

Use (a) the Trapezoidal Rule and (b) Simpson's Rule to approximate the integral to four decimal places. Compare your results with the exact value.

Evaluate the integral.

Find the integral.

Evaluate the integral.

Evaluate the integral.

Use the Trapezoidal Rule to approximate the integral with answers rounded to four decimal places.

Write the form of the partial fraction decomposition of the rational expression. Do not find the numerical values of the constants. $Write the form of the partial fraction decomposition of the rational expression. Do not find the numerical values of the constants. A) B) C) D)$

Make a substitution to express the integrand as a rational function and then evaluate the integral. Round the answer to four decimal places.

Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule with n subintervals.

The region is represented below. Find the area of this region to two decimal places.

Evaluate the integral.

A particle moves on a straight line with velocity function . Find its position function .

Find the integral.

Find the integral.

Evaluate the integral.

Use a table of integrals to evaluate the integral.