Question 1

Use the properties of summation and Theorem 4.2 to evaluate the sum.

Accepted Answer

A) 4930 
B) 335 
C) 10,409 
D) 5555 
E) 5533 
A) 4930 
B) 335 
C) 10,409 
D) 5555 
E) 5533 D

Question 2

Determine the area of the given region.

Accepted Answer

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

Question 3

Evaluate the following definite integral by the limit definition.

Accepted Answer

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

Question 4

The graph of the function   is given below. Which of the following definite integrals yields the area of the shaded region?

Accepted Answer

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

Question 5

Find the indefinite integral   .

Accepted Answer

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

Question 6

Find the indefinite integral of the following function and check the result by differentiation.

Accepted Answer

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

Question 7

The rate of growth   of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days   That is,   . The initial size of the population is 300. After one day the population has grown to 400. Estimate the population after 9 days. Round your answer to the nearest integer.

Accepted Answer

A)    bacteria 
B)    bacteria 
C)    bacteria 
D)    bacteria 
E)    bacteria 
A)    bacteria 
B)    bacteria 
C)    bacteria 
D)    bacteria 
E)    bacteria

Question 8

Evaluate the integral   given

Accepted Answer

A) 12 
B) 18 
C) 28 
D) -18 
E) 45 
A) 12 
B) 18 
C) 28 
D) -18 
E) 45

Question 9

Solve the differential equation.

Accepted Answer

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

Question 10

Find the indefinite integral   .

Accepted Answer

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

Question 11

Solve the differential equation.

Accepted Answer

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

Question 12

Find the general solution of the differential equation below and check the result by differentiation.

Accepted Answer

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

Question 13

Use the summation formulas to rewrite the expression   without the summation notation.

Accepted Answer

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

Question 14

Write the limit   as a definite integral on the interval   where    is any point in the   subinterval.

Accepted Answer

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

Question 15

Write the following limit as a definite integral on the interval [5 , 11], where ci is any point in the ith subinterval.

Accepted Answer

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

Question 16

The rate of depreciation   of a machine is inversely proportional to the square of   where V is the value of the machine t years after it was purchased. The initial value of the machine was   and its value decreased   in the first year. Estimate its value after 5 years. Round your answer to the nearest integer.

Accepted Answer

A) $500,000 
B) $285,714 
C) $571,428 
D) $485,714 
E) $371,429 
A) $500,000 
B) $285,714 
C) $571,428 
D) $485,714 
E) $371,429

Question 17

Find the indefinite integral   .

Accepted Answer

A)    
B)    
C)    
D)    
E) none of the above 
A)    
B)    
C)    
D)    
E) none of the above

Question 18

The total cost C (in dollars) of purchasing and maintaining a piece of equipment for x years is   Perform the integration to write C as a function of x.

Accepted Answer

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

Question 19

The rate of disbursement   of a 2 million dollar federal grant is proportional to the square of   Time t is measured in days   and   is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 60 days. Assume that all the money will be disbursed in 200 days.

Accepted Answer

A) $686,000 
B) $1,029,000 
C) $50,700 
D) $16,900 
E) $25,350 
A) $686,000 
B) $1,029,000 
C) $50,700 
D) $16,900 
E) $25,350

Question 20

Use a computer algebra system and Simpson's Rule with   to approximate t in the integral equation   . Round your answer to three decimal places.

Accepted Answer

A) 6.385 
B) 6.045 
C) 5.715 
D) 6.008 
E) 5.985 
A) 6.385 
B) 6.045 
C) 5.715 
D) 6.008 
E) 5.985

Use the properties of summation and Theorem 4.2 to evaluate the sum.

Determine the area of the given region.

Evaluate the following definite integral by the limit definition.

The graph of the function is given below. Which of the following definite integrals yields the area of the shaded region?

Find the indefinite integral .

Find the indefinite integral of the following function and check the result by differentiation.

Evaluate the integral given

Solve the differential equation.

Find the indefinite integral .

Solve the differential equation.

Find the general solution of the differential equation below and check the result by differentiation.

Use the summation formulas to rewrite the expression without the summation notation.

Write the limit as a definite integral on the interval where is any point in the subinterval.

Write the following limit as a definite integral on the interval [5 , 11], where c_iis any point in the ith subinterval.

Find the indefinite integral .

The total cost C (in dollars) of purchasing and maintaining a piece of equipment for x years is Perform the integration to write C as a function of x.

The rate of disbursement of a 2 million dollar federal grant is proportional to the square of Time t is measured in days and is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 60 days. Assume that all the money will be disbursed in 200 days.

Use a computer algebra system and Simpson's Rule with to approximate t in the integral equation . Round your answer to three decimal places.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Exam 7: Integration

Use the properties of summation and Theorem 4.2 to evaluate the sum.

Determine the area of the given region.

Evaluate the following definite integral by the limit definition.

The graph of the function is given below. Which of the following definite integrals yields the area of the shaded region?

Find the indefinite integral .

Find the indefinite integral of the following function and check the result by differentiation.

Evaluate the integral given

Solve the differential equation.

Find the indefinite integral .

Solve the differential equation.

Find the general solution of the differential equation below and check the result by differentiation.

Use the summation formulas to rewrite the expression without the summation notation.

Write the limit as a definite integral on the interval where is any point in the subinterval.

Write the following limit as a definite integral on the interval [5 , 11], where ci is any point in the ith subinterval.

Find the indefinite integral .

The total cost C (in dollars) of purchasing and maintaining a piece of equipment for x years is Perform the integration to write C as a function of x.

The rate of disbursement of a 2 million dollar federal grant is proportional to the square of Time t is measured in days and is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 60 days. Assume that all the money will be disbursed in 200 days.

Use a computer algebra system and Simpson's Rule with to approximate t in the integral equation . Round your answer to three decimal places.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Write the following limit as a definite integral on the interval [5 , 11], where c_iis any point in the ith subinterval.