Question 1

Evaluate the integral  . ​

Accepted Answer

B

Question 2

Evaluate the integral  . ​

Accepted Answer

D

Question 3

If the marginal revenue (in dollars per unit) for a month is given by  , find the total revenue from the sale of 125 units to the nearest cent. ​

Accepted Answer

To find the total revenue, we need to integrate the given marginal revenue function:

Total Revenue = ∫MR(q) dq

Total Revenue = ∫(140 - 0.8q) dq   (given MR = 140 - 0.8q)

Total Revenue = [140q - 0.4q^2] / 2 + C

We need to find the constant of integration (C) using the fact that revenue is 0 when q = 0:

0 = [140(0) - 0.4(0)^2] / 2 + C

C = 0

So the final expression for total revenue is:

Total Revenue = [140q - 0.4q^2] / 2

To find the total revenue from the sale of 125 units, we substitute q = 125 in the above expression:

Total Revenue = [140(125) - 0.4(125)^2] / 2

Total Revenue ≈ $5,195.31 (rounded to the nearest cent)

Therefore, the best choice is (C).

Question 4

Find a function g(x) such that  . ​

Accepted Answer

The answer of Find a function g(x) such that ...

Question 5

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 4,200 feet high when  seconds, write the formula for the height of the particle at any time t.

Accepted Answer

The answer of Suppose that a particle has been shot...

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

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 11

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 12

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 13

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

Accepted Answer

Rewrite the integrand using algebra:

$$\frac{x + 2}{(x - 1)^2} = \frac{x - 1}{(x - 1)^2} + \frac{3}{(x - 1)^2} = \frac{1}{x - 1} + \frac{3}{(x - 1)^2}$$

Integrate using the power rule:

$$\int \frac{x + 2}{(x - 1)^2} dx = \int \left(\frac{1}{x - 1} + \frac{3}{(x - 1)^2}\right) dx = \ln|x - 1| - \frac{3}{x - 1} + C$$

where C is the constant of integration.

Therefore, the correct answer is B.

Question 14

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 15

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 16

If  , find  . ​

Accepted Answer

The answer of If  , find  . ​
...

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

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 20

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Quiz 13: Indefinite Integrals

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 125 units to the nearest cent.

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 4,200 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 .

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.

Evaluate the integral .

Evaluate the integral .

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

Evaluate the integral .

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) .

If , find .

Evaluate the integral .

Evaluate the integral .

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.

Evaluate the integral .

Quiz 13: Indefinite Integrals

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 125 units to the nearest cent. ​

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 4,200 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 . ​

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. ​

Evaluate the integral . ​

Evaluate the integral . ​

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

Evaluate the integral . ​

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) . ​

If , find . ​

Evaluate the integral . ​

Evaluate the integral . ​

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. ​ ​ ​

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 125 units to the nearest cent.

Find a function g(x) such that .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

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.

Evaluate the integral .

Evaluate the integral .

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

Evaluate the integral .

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) .

If , find .

Evaluate the integral .

Evaluate the integral .

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.

Evaluate the integral .