Question 1

Use Riemann sums and a limit to compute the exact area under the curve.   on

Accepted Answer

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

Question 2

Determine the number of steps to guarantee an accuracy of 10-4 using (a) the Trapezoidal Rule (b) the Midpoint Rule and (c) Simpson's Rule.

Accepted Answer

A)  a. 48 
b. 34
c.  4 
B)  a. 48 
b. 34
c.  14 
C)  a. 23 
b. 16
c.  4 
D)  a. 23 
b. 16
c. 14 
A)  a. 48 
b. 34
c.  4 
B)  a. 48 
b. 34
c.  14 
C)  a. 23 
b. 16
c.  4 
D)  a. 23 
b. 16
c. 14

Question 3

Evaluate the integral.

Accepted Answer

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

Question 4

Translate the following calculation into summation notation and then compute the sum. Round to two decimal places. The square root of the sum of the first   positive integers.

Accepted Answer

A)    sum =   
B)    sum =   
C)      
D)    
A)    sum =   
B)    sum =   
C)      
D)

Question 5

Use summation rules to compute the sum.

Accepted Answer

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

Question 6

Write the given (total) area as an integral or sum of integrals. The area between   and the   -axis for   .

Accepted Answer

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

Question 7

Evaluate the definite integral.

Accepted Answer

A)    
B)    
C)    
D)  0 
A)    
B)    
C)    
D)  0

Question 8

Use summation rules to compute the sum.

Accepted Answer

A)  4130 
B)  69,300 
C)  72,891 
D)  4301 
A)  4130 
B)  69,300 
C)  72,891 
D)  4301

Question 9

Write the expression as a single integral.

Accepted Answer

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

Use Riemann sums and a limit to compute the exact area under the curve. on

Determine the number of steps to guarantee an accuracy of 10^-4 using (a) the Trapezoidal Rule (b) the Midpoint Rule and (c) Simpson's Rule.

Evaluate the integral.

Translate the following calculation into summation notation and then compute the sum. Round to two decimal places. The square root of the sum of the first positive integers.

Use summation rules to compute the sum.

Write the given (total) area as an integral or sum of integrals. The area between and the -axis for .

Evaluate the definite integral.

Use summation rules to compute the sum.

Write the expression as a single integral.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

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 5: Integration

Use Riemann sums and a limit to compute the exact area under the curve. on

Determine the number of steps to guarantee an accuracy of 10-4 using (a) the Trapezoidal Rule (b) the Midpoint Rule and (c) Simpson's Rule.

Evaluate the integral.

Translate the following calculation into summation notation and then compute the sum. Round to two decimal places. The square root of the sum of the first positive integers.

Use summation rules to compute the sum.

Write the given (total) area as an integral or sum of integrals. The area between and the -axis for .

Evaluate the definite integral.

Use summation rules to compute the sum.

Write the expression as a single integral.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

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

Determine the number of steps to guarantee an accuracy of 10^-4 using (a) the Trapezoidal Rule (b) the Midpoint Rule and (c) Simpson's Rule.