Question 1

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 2

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 3

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Accepted Answer

A)  converges to   
B)  converges to   
C)  converges to   
D)  diverges 
A)  converges to   
B)  converges to   
C)  converges to   
D)  diverges

Question 4

Find

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

Find the limit.

Accepted Answer

A)  0 
B)  1 
C)  5 
D)  -5 
A)  0 
B)  1 
C)  5 
D)  -5

Question 6

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral.  ...

Question 8

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Suppose the size of a particular animal's pupils expand and contract depending on the amount of light available. Let   be the size in mm of the pupils at light intensity x. Find the smallest possible size of the pupils by finding

Accepted Answer

A)  1 mm 
B)  10 mm 
C)  20 mm 
D)    mm 
A)  1 mm 
B)  10 mm 
C)  20 mm 
D)    mm

Question 10

Determine if l'Hopital's Rule applies.

Accepted Answer

A)  yes 
B)  no 
A)  yes 
B)  no

Question 11

Evaluate the integral. (Hint: you may need to use a reduction formula.)

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral.  ...

Question 14

Find the limit.

Accepted Answer

A)  0 
B)  1 
C)  -3 
D)  3 
A)  0 
B)  1 
C)  -3 
D)  3

Question 15

The pdf describing the chance that a given insect will die at a particular age, x days, is   . What is the chance the insect will live between 1 and 5 days? Round your answer three decimal places.

Accepted Answer

A)  0.287 
B)  0.622 
C)  0.910 
D)  0.524 
A)  0.287 
B)  0.622 
C)  0.910 
D)  0.524

Question 16

Is the function   a probablilty density function on the interval   ?

Accepted Answer

A)  Yes 
B)  No, because the integral of the probability is not 1 
C)  No, because the function can be negative in the range 
A)  Yes 
B)  No, because the integral of the probability is not 1 
C)  No, because the function can be negative in the range

Question 17

Find an antiderivative.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

Evaluate the integral.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

Find the error in the following incorrect calculation.

Accepted Answer

The first application of l'Hôpital's Rul

Question 20

In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Evaluate the integral.

Evaluate the integral.

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Find

Find the limit.

Evaluate the integral.

Evaluate the integral.

Evaluate the integral.

Suppose the size of a particular animal's pupils expand and contract depending on the amount of light available. Let be the size in mm of the pupils at light intensity x. Find the smallest possible size of the pupils by finding

Determine if l'Hopital's Rule applies.

Evaluate the integral. (Hint: you may need to use a reduction formula.)

You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).

Evaluate the integral.

Find the limit.

The pdf describing the chance that a given insect will die at a particular age, x days, is . What is the chance the insect will live between 1 and 5 days? Round your answer three decimal places.

Is the function a probablilty density function on the interval ?

Find an antiderivative.

Evaluate the integral.

Find the error in the following incorrect calculation.

In an AC circuit, the current has the form for constants The power is defined as for a constant . Find the average value of the power by integrating over the interval

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 8: Integration Techniques

Evaluate the integral.

Evaluate the integral.

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Find

Find the limit.

Evaluate the integral.

Evaluate the integral.

Evaluate the integral.

Suppose the size of a particular animal's pupils expand and contract depending on the amount of light available. Let be the size in mm of the pupils at light intensity x. Find the smallest possible size of the pupils by finding

Determine if l'Hopital's Rule applies.

Evaluate the integral. (Hint: you may need to use a reduction formula.)

You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).

Evaluate the integral.

Find the limit.

The pdf describing the chance that a given insect will die at a particular age, x days, is . What is the chance the insect will live between 1 and 5 days? Round your answer three decimal places.

Is the function a probablilty density function on the interval ?

Find an antiderivative.

Evaluate the integral.

Find the error in the following incorrect calculation.

In an AC circuit, the current has the form for constants The power is defined as for a constant . Find the average value of the power by integrating over the interval

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters