Question 1

Find the indefinite integral. Hint: Let  .

Accepted Answer

The answer of Find the indefinite integral. Hint: Let ...

Question 2

Find the indefinite integral. Hint: Let  .

Accepted Answer

Let u = 11eaa8b1_dab3_8fab_b1b6_01973e1424bd_TB6026_11, then du = 11eaa8b1_dab3_b6bc_b1b6_dd8559abc81b_TB6026_11 dx. The integral then becomes ∫ 1/u du, which is ln|u| + C. Substituting back in for u gives ln|11eaa8b1_dab3_8fab_b1b6_01973e1424bd_TB6026_11| + C, which simplifies to ln|u| + C.

Question 3

Find the indefinite integral.

Accepted Answer

The indefinite integral of $e^{ax}\cos bx$ is $\frac{e^{ax}}{a^2+b^2}(a\cos bx + b\sin bx) + C$. In this case, $a=11$ and $b=-3$, so the indefinite integral is $\frac{e^{11x}}{11^2+(-3)^2}(11\cos (-3x) - 3\sin (-3x)) + C$. Simplifying gives $\frac{e^{11x}}{130}(11\cos 3x + 3\sin 3x) + C$, which matches choice (B).

Question 4

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
...

Question 5

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
...

Question 6

In calm waters the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that is circular in shape. If the radius r of the circle is increasing at the rate of  feet/minute t minutes after the rupture occurs. Find an expression for the radius at any time t. Hint:  .
How large is the polluted area 30 minutes after the rupture occurred?

Accepted Answer

The answer of In calm waters the oil spilling from...

Question 7

The population of a certain city is projected to grow at the rate of  people/year, t years from now. The current population is 70,000. What will be the population 5 years from now?
__________ people

Accepted Answer

The answer of The population of a certain city is...

Question 8

Find the indefinite integral.

Accepted Answer

The integral of e^x is simply e^x plus a constant of integration.

Question 9

Find the indefinite integral. Hint:  implies  .

Accepted Answer

The answer of Find the indefinite integral. Hint:  implies...

Question 10

The registrar of University estimates that the total student enrollment in the Continuing Education division will grow at the rate of  students/year t years from now. If the current student enrollment is 4,000, find an expression giving the total student enrollment t years from now.
What will be the student enrollment be 5 years from now?

Accepted Answer

The answer of The registrar of University estimates that the...

Question 11

The population of a certain city is projected to grow at the rate of  people/year, t years from now. The current population is 40,000. What will be the population 3 years from now?

Accepted Answer

The answer of The population of a certain city is...

Question 12

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
...

Question 13

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x)) is f'(x) and that the graph of f passes through the given point.

Accepted Answer

Let's integrate the given slope to obtain the function f: ∫f'(x) dx = ∫f(x) dx = ∫f(x) f'(x) dx = ∫f(x) dx + C where C is the constant of integration. Thus, we have that f(x) = Ce^(x^2/2) (since integrating f'(x) with respect to x gives us e^(x^2/2) up to a constant C.) Now, using the given point (0,1), we have 1 = f(0) = Ce^(0) = C, so f(x) = e^(x^2/2). Thus, the correct choice is D.

Question 14

The average student enrolled in the 20-week Court Reporting I course at the American Institute of Court Reporting progresses according to the rule  where  measures the rate of change in the number of words/minute of dictation the student takes in machine shorthand after  weeks in the course. Assuming that the average student enrolled in this course begins with a dictation speed of 60 words/minute, find an expression  that gives the dictation speed of the student after  weeks in the course.

Accepted Answer

The answer of The average student enrolled in the 20-week...

Question 15

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
...

Question 16

Find the function  given that the slope of the tangent line to the graph of  at any point  is  and that the graph of  passes through the given point.

Accepted Answer

The answer of Find the function  given that the...

Question 17

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x)) is f'(x) and that the graph of f passes through the given point.

Accepted Answer

The answer of Find the function f given that the...

Question 18

The registrar of Kellog University estimates that the total student enrollment in the Continuing Education division will grow at the rate of  students/year  years from now. The current student enrollment is 500. What will be the student enrollment 7 years from now?

Accepted Answer

The answer of The registrar of Kellog University estimates that...

Question 19

A drug is carried into an organ of volume   by a liquid that enters the organ at the rate of  and leaves it at the rate of  . The concentration of the drug in the liquid entering the organ is  . If the concentration of the drug in the organ at time  is increasing at the rate of   , and the concentration of the drug in the organ initially is  , find the concentration of the drug in the organ at time  .

Accepted Answer

The answer of A drug is carried into an organ...

Question 20

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
...

Quiz 6: Integration

Find the indefinite integral. Hint: Let .

Find the indefinite integral. Hint: Let .

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

The population of a certain city is projected to grow at the rate of people/year, t years from now. The current population is 70,000. What will be the population 5 years from now? __________ people

Find the indefinite integral.

Find the indefinite integral. Hint: implies .

The population of a certain city is projected to grow at the rate of people/year, t years from now. The current population is 40,000. What will be the population 3 years from now?

Find the indefinite integral.

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f'(x) and that the graph of f passes through the given point.

Find the indefinite integral.

Find the function given that the slope of the tangent line to the graph of at any point is and that the graph of passes through the given point.

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f'(x) and that the graph of f passes through the given point.

The registrar of Kellog University estimates that the total student enrollment in the Continuing Education division will grow at the rate of students/year years from now. The current student enrollment is 500. What will be the student enrollment 7 years from now?

Find the indefinite integral.

Quiz 6: Integration

Find the indefinite integral. Hint: Let .

Find the indefinite integral. Hint: Let .

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

The population of a certain city is projected to grow at the rate of people/year, t years from now. The current population is 70,000. What will be the population 5 years from now? __________ people

Find the indefinite integral.

Find the indefinite integral. Hint: implies .

The population of a certain city is projected to grow at the rate of people/year, t years from now. The current population is 40,000. What will be the population 3 years from now?

Find the indefinite integral.

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f '(x) and that the graph of f passes through the given point.

Find the indefinite integral.

Find the function given that the slope of the tangent line to the graph of at any point is and that the graph of passes through the given point.

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f '(x) and that the graph of f passes through the given point.

The registrar of Kellog University estimates that the total student enrollment in the Continuing Education division will grow at the rate of students/year years from now. The current student enrollment is 500. What will be the student enrollment 7 years from now?

Find the indefinite integral.

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f'(x) and that the graph of f passes through the given point.

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f'(x) and that the graph of f passes through the given point.