Question 1

The marginal revenue for a new calculator is given by  , where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators. ​

Accepted Answer

To find the total revenue function, we need to integrate the marginal revenue function. Integrating 11ea984b_b172_5295_9029_65cb072f354c_TB4005_11 with respect to x gives:
R(x) = ∫(11x) dx = 11/2 x^2 + C
where C is the constant of integration. Since the revenue is 0 when the number of calculators is 0, we have:
0 = 11/2 (0)^2 + C
C = 0
Therefore, the total revenue function is:
R(x) = 11/2 x^2
which simplifies to:
R(x) = 5.5x^2
The closest choice to this function is option C: 11ea984b_b172_79a8_9029_7b6ead28ab20_TB4005_11.

Question 2

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 3

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 4

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 5

If  , find  . ​

Accepted Answer

The answer of If  , find  . ​
...

Question 6

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 7

Find du if  . ​

Accepted Answer

The answer of Find du if  . ​
...

Question 8

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 9

Which of the following integrals cannot be integrated by using the methods studied so far? ​
(a)  ​​
(b)  ​
(c)  ​
(d)  ​
(e)  ​

Accepted Answer

Option (a) can be integrated using integration by substitution.

Option (b) can be integrated using integration by parts.

Option (c) can be integrated using partial fractions.

Option (d) can be integrated using trigonometric substitution.

Option (e) cannot be integrated using the methods studied so far, such as substitution, integration by parts, partial fractions, or trigonometric substitution. Therefore, our answer is (B) a, b, e.

Question 10

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 11

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 12

Suppose an oil tanker hits a reef and begins to leak. The efforts of the workers repairing the leak cause the rate at which the oil is leaking to decrease. The oil was leaking at a rate of 39 barrels per hour at the end of the first hour after the accident, and the rate is decreasing at a rate of one barrel per hour. How many barrels of oil will leak in the first 6 hours? ​

Accepted Answer

The answer of Suppose an oil tanker hits a reef...

Question 13

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 14

The total physical output of a number of machines or workers is called physical productivity and is a function of the number of machines or workers. If  is the productivity,  is the marginal physical productivity. If the marginal physical productivity for bricklayers is  , where P is the number of bricks laid per day and x is the number of bricklayers, find the physical productivity of 5 bricklayers. (Note:  when  .) ​

Accepted Answer

The answer of The total physical output of a number...

Question 15

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 16

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2). ​  ​

Accepted Answer

Integrating the given expression, we get:

$$\int\frac{1}{x-1} dx = \ln|x-1| + C$$

This represents a family of logarithmic curves. To find the value of the constant $C$, we use the given point (1,2):

$$\ln|1-1|+C = \ln|0|+C$$

This is undefined, so the curve cannot pass through the point (1,2).

Therefore, the correct answer is B, as none of the curves in the family pass through the given point.

Question 17

Write the indefinite integral that gives the family associated with  . ​

Accepted Answer

The indefinite integral generates a constant of integration which can be any value, and therefore it is not possible to determine the specific family associated with this integral. Therefore, the choice which only differs in the last hexadecimal digit (8f3d vs 8f3e) is the best choice as it is the most similar to the given integral.

Question 18

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Question 19

Suppose an oil tanker hits a reef and begins to leak. The efforts of the workers repairing the leak cause the rate at which the oil is leaking to decrease. The oil was leaking at a rate of 41 barrels per hour at the end of the first hour after the accident, and the rate is decreasing at a rate of one barrel per hour. What formula describes the rate of loss in terms of the time t that has lapsed since the leak began? ​

Accepted Answer

The answer of Suppose an oil tanker hits a reef...

Question 20

Evaluate the integral  . ​

Accepted Answer

The answer of Evaluate the integral  . ​
...

Quiz 12: Indefinite Integrals

The marginal revenue for a new calculator is given by , where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

If , find .

Evaluate the integral .

Find du if .

Evaluate the integral .

Which of the following integrals cannot be integrated by using the methods studied so far? (a) (b) (c) (d) (e)

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2) .

Write the indefinite integral that gives the family associated with .

Evaluate the integral .

Evaluate the integral .

Quiz 12: Indefinite Integrals

The marginal revenue for a new calculator is given by , where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators. ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​

If , find . ​

Evaluate the integral . ​

Find du if . ​

Evaluate the integral . ​

Which of the following integrals cannot be integrated by using the methods studied so far? ​ (a) ​​ (b) ​ (c) ​ (d) ​ (e) ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2) . ​ ​

Write the indefinite integral that gives the family associated with . ​

Evaluate the integral . ​

Evaluate the integral . ​

The marginal revenue for a new calculator is given by , where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

If , find .

Evaluate the integral .

Find du if .

Evaluate the integral .

Which of the following integrals cannot be integrated by using the methods studied so far? (a) (b) (c) (d) (e)

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2) .

Write the indefinite integral that gives the family associated with .

Evaluate the integral .

Evaluate the integral .