Question 1

Evaluate the integral  . ​

Accepted Answer

C

Question 2

If  , find  . ​

Accepted Answer

A

Question 3

Find a function g(x) such that  . ​

Accepted Answer

A

Question 4

Suppose that a particle has been shot into the air in such a way that the rate at which its height H (in feet per second) is changing is  . If the particle is 3,100 feet high when  seconds, write the formula for the height of the particle at any time t.

Accepted Answer

The given information is the rate of change of height, which is the derivative of the height function. Therefore, we need to find the antiderivative (or integral) of the given function to obtain the height function. Integrating 11ea984b_b163_5f08_9029_d779edb0c9fe_TB4005_11 with respect to t gives 11ea984b_b163_ad2b_9029_a9e1a827d599_TB4005_11 + C, where C is a constant of integration. We can find the value of C using the fact that the particle is 3,100 feet high when t=11ea984b_b163_8619_9029_95da000015c7_TB4005_11, so we plug in t=11ea984b_b163_8619_9029_95da000015c7_TB4005_11 and H=3,100 into the height function: 3,100 = 11ea984b_b163_ad2b_9029_a9e1a827d599_TB4005_11(11ea984b_b163_8619_9029_95da000015c7_TB4005_11) + C. Solving for C, we get C=3,100 - 11ea984b_b163_ad2b_9029_a9e1a827d599_TB4005_11(11ea984b_b163_8619_9029_95da000015c7_TB4005_11) = 11ea984b_b163_d43c_9029_9bd1eeb26232_TB4005_11. Therefore, the height function is H(t) = 11ea984b_b163_ad2b_9029_a9e1a827d599_TB4005_11t + 11ea984b_b163_d43c_9029_9bd1eeb26232_TB4005_11, which matches choice B.

Question 5

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 6

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 7

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 8

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 9

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 10

If the marginal revenue (in dollars per unit) for a month is given by  , find the total revenue from the sale of 150 units to the nearest cent. ​

Accepted Answer

The answer of If the marginal revenue (in dollars per...

Question 11

Use algebra to rewrite the integrand; then integrate and simplify. ​  ​

Accepted Answer

The answer of Use algebra to rewrite the integrand; then...

Question 12

The DeWitt Company has found that the rate of change of its average cost of producing a product is  , where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00. Find the average cost of producing 140 units of the product. Round to the nearest dollar. ​

Accepted Answer

The answer of The DeWitt Company has found that the...

Question 13

A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family. ​  ​  ​

Accepted Answer

The answer of A family of functions is given and...

Question 14

Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t). If the rate at which action potentials are produced is  , and if there are 0 action potentials when  , find the formula for P(t). ​

Accepted Answer

The answer of Suppose that when a sense organ receives...

Question 15

Use algebra to rewrite the integrand; then integrate and simplify. ​  ​

Accepted Answer

The answer of Use algebra to rewrite the integrand; then...

Question 16

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 17

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 18

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

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  . ​
...

Quiz 12: Indefinite Integrals

Evaluate the integral .

If , find .

Find a function g(x) such that .

Suppose that a particle has been shot into the air in such a way that the rate at which its height H (in feet per second) is changing is . If the particle is 3,100 feet high when seconds, write the formula for the height of the particle at any time t.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

If the marginal revenue (in dollars per unit) for a month is given by , find the total revenue from the sale of 150 units to the nearest cent.

Use algebra to rewrite the integrand; then integrate and simplify.

The DeWitt Company has found that the rate of change of its average cost of producing a product is , where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00. Find the average cost of producing 140 units of the product. Round to the nearest dollar.

A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family.

Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t) . If the rate at which action potentials are produced is , and if there are 0 action potentials when , find the formula for P(t) .

Use algebra to rewrite the integrand; then integrate and simplify.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Quiz 12: Indefinite Integrals

Evaluate the integral . ​

If , find . ​

Find a function g(x) such that . ​

Suppose that a particle has been shot into the air in such a way that the rate at which its height H (in feet per second) is changing is . If the particle is 3,100 feet high when seconds, write the formula for the height of the particle at any time t.

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​

If the marginal revenue (in dollars per unit) for a month is given by , find the total revenue from the sale of 150 units to the nearest cent. ​

Use algebra to rewrite the integrand; then integrate and simplify. ​ ​

The DeWitt Company has found that the rate of change of its average cost of producing a product is , where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00. Find the average cost of producing 140 units of the product. Round to the nearest dollar. ​

A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family. ​ ​ ​

Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t) . If the rate at which action potentials are produced is , and if there are 0 action potentials when , find the formula for P(t) . ​

Use algebra to rewrite the integrand; then integrate and simplify. ​ ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​​

Evaluate the integral . ​

Evaluate the integral .

If , find .

Find a function g(x) such that .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

If the marginal revenue (in dollars per unit) for a month is given by , find the total revenue from the sale of 150 units to the nearest cent.

Use algebra to rewrite the integrand; then integrate and simplify.

The DeWitt Company has found that the rate of change of its average cost of producing a product is , where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00. Find the average cost of producing 140 units of the product. Round to the nearest dollar.

A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family.

Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t) . If the rate at which action potentials are produced is , and if there are 0 action potentials when , find the formula for P(t) .

Use algebra to rewrite the integrand; then integrate and simplify.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .