Question 1

Evaluate the integral using the indicated trigonometric substitution.

Accepted Answer

The answer of Evaluate the integral using the indicated trigonometric...

Question 2

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

Accepted Answer

A) 0.2326 
B) 0.1088 
C) 0.1163 
D) 0.2029

Question 3

A body moves along a coordinate line in such a way that its velocity at any time t, where  , is given by  .
Find its position function if it is initially located at the origin.

Accepted Answer

The answer of A body moves along a coordinate line...

Question 4

Find the integral.

Accepted Answer

The answer of Find the integral. ...

Question 5

Find the integral using an appropriate trigonometric substitution.

Accepted Answer

A)   
B)   
C)   
D)

Question 6

Evaluate the integral to six decimal places.

Accepted Answer

The answer of Evaluate the integral to six decimal places....

Question 7

Determine whether the improper integral converges or diverges, and if it converges, find its value.

Accepted Answer

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

Question 8

Use the Table of Integrals to evaluate the integral to three decimal places.

Accepted Answer

The answer of Use the Table of Integrals to evaluate...

Question 9

Let a and b be real numbers. What integral must appear in place of the question mark "?" to make the following statement true?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Find the integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 11

Find the integral using an appropriate trigonometric substitution.

Accepted Answer

A)   
B)   
C)   
D)

Question 12

Find the integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 13

Use the Trapezoidal Rule to approximate  for  . Round the result to four decimal places.

Accepted Answer

The answer of Use the Trapezoidal Rule to approximate ...

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 to one decimal place.

Accepted Answer

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

Question 15

Find the integral.

Accepted Answer

The answer of Find the integral. ...

Question 16

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

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

Accepted Answer

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

Question 18

Evaluate the integral or show that it is divergent.

Accepted Answer

The answer of Evaluate the integral or show that it...

Question 19

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 20

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Exam 7: Techniques of Integration

Evaluate the integral using the indicated trigonometric substitution.

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

A body moves along a coordinate line in such a way that its velocity at any time t, where , is given by . Find its position function if it is initially located at the origin.

Find the integral.

Find the integral using an appropriate trigonometric substitution.

Evaluate the integral to six decimal places.

Determine whether the improper integral converges or diverges, and if it converges, find its value.

Use the Table of Integrals to evaluate the integral to three decimal places.

Let a and b be real numbers. What integral must appear in place of the question mark "?" to make the following statement true?

Find the integral.

Find the integral using an appropriate trigonometric substitution.

Find the integral.

Use the Trapezoidal Rule to approximate for . Round the result to four decimal places.

Find the integral.

Evaluate the integral.

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

Evaluate the integral or show that it is divergent.

Evaluate the integral.

Evaluate the integral.