Question 1

Evaluate the following improper integral whenever it is convergent.  Enter divergent if the integral is divergent.

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Question 2

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Find the exact value of the integral. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use the trapezoidal rule and Simpson's rule...

Question 3

The present value of a perpetual stream of income that flows continually at the rate of  dollars per year is given by the formula  where  is the interest rate compounded continuously. Using this formula, find the present value of a perpetual net income stream that is generated at the rate of  dollars per year.
Hint:  .

Accepted Answer

The answer of The present value of a perpetual stream...

Question 4

Evaluate the following improper integral whenever it is convergent.

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Question 5

Find the area of the region bounded by the x-axis and the graph of the function

Accepted Answer

The answer of Find the area of the region bounded...

Question 6

Evaluate the following improper integral whenever it is convergent.  Enter divergent if the integral is divergent.

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Question 7

A university alumni group wishes to provide an annual scholarship in the amount of $1,300 beginning next year. If the scholarship fund will earn an interest rate of 8% / year compounded continuously, find the amount of the endowment the alumni are required to make now.
$__________

Accepted Answer

The answer of A university alumni group wishes to provide...

Question 8

Becky Wilkinson wants to establish a trust fund that will provide her children and heirs with a perpetual annuity in the amount of  thousand dollars per year beginning next year. If the trust fund will earn an interest rate of 10% per year compounded continuously, find the amount that she must place in the trust fund now.
Hint: Use the formula  .
$ __________ thousand dollars.

Accepted Answer

The answer of Becky Wilkinson wants to establish a trust...

Question 9

Find the area of the region under the given curve  over the indicated interval.

Accepted Answer

The answer of Find the area of the region under...

Question 10

Evaluate the improper integral whenever it is convergent. If not, enter divergent.

Accepted Answer

The answer of Evaluate the improper integral whenever it is...

Question 11

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Find the exact value of the integral. 
A) 
B) 
C) 
D)

Accepted Answer

Using the trapezoidal rule with $n=4$, we get:

$$\begin{aligned} \int_{-1}^1e^x\ dx &\approx \frac{1}{2}\left[f(-1)+2f\left(-\frac{1}{2}ight)+2f\left(\frac{1}{2}ight)+f(1)ight]\ &= \frac{1}{2}\left[e^{-1}+2e^{-1/2}+2e^{1/2}+eight]\ &= 2.233665\end{aligned}$$

Using Simpson's rule with $n=4$, we get:

$$\begin{aligned} \int_{-1}^1e^x\ dx &\approx \frac{1}{3}\left[f(-1)+4f\left(-\frac{1}{2}ight)+2f(0)+4f\left(\frac{1}{2}ight)+f(1)ight]\ &= \frac{1}{3}\left[e^{-1}+4e^{-1/2}+2+4e^{1/2}+eight]\ &= 2.350402\end{aligned}$$

The exact value of the integral is:

$$\begin{aligned} \int_{-1}^1e^x\ dx = e- \frac{1}{e} = 2.350402\end{aligned}$$

Therefore, the best choice is $\boxed{	extbf{(C)}}$.

Question 12

Evaluate the following improper integral whenever it is convergent.  Enter divergent if the integral is divergent.

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Question 13

Find the area of the region under the given curve  over the indicated interval.

Accepted Answer

The answer of Find the area of the region under...

Question 14

Determine whether the statement is true.
If  exists, then  exists and  .
Answer yes or no.

Accepted Answer

The answer of Determine whether the statement is true.
If ...

Question 15

Evaluate the following improper integral whenever it is convergent.

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Question 16

Evaluate the following improper integral whenever it is convergent.  Enter divergent if the integral is divergent.

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Question 17

Find the area of the region under the given curve  over the indicated interval.

Accepted Answer

The answer of Find the area of the region under...

Question 18

Evaluate the improper integral if it is convergent.

Accepted Answer

The answer of Evaluate the improper integral if it is...

Question 19

Evaluate the following improper integral whenever it is convergent.  Enter divergent if the integral is divergent.

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Question 20

Evaluate the following improper integral whenever it is convergent.  Enter divergent if the integral is divergent.

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Quiz 7: Additional Topics in Integration

Evaluate the following improper integral whenever it is convergent. Enter divergent if the integral is divergent.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Find the exact value of the integral.

Evaluate the following improper integral whenever it is convergent.

Find the area of the region bounded by the x-axis and the graph of the function

Evaluate the following improper integral whenever it is convergent. Enter divergent if the integral is divergent.

A university alumni group wishes to provide an annual scholarship in the amount of $1,300 beginning next year. If the scholarship fund will earn an interest rate of 8% / year compounded continuously, find the amount of the endowment the alumni are required to make now. $__________

Find the area of the region under the given curve over the indicated interval.

Evaluate the improper integral whenever it is convergent. If not, enter divergent.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Find the exact value of the integral.

Evaluate the following improper integral whenever it is convergent. Enter divergent if the integral is divergent.

Find the area of the region under the given curve over the indicated interval.

Determine whether the statement is true. If exists, then exists and . Answer yes or no.

Evaluate the following improper integral whenever it is convergent.

Evaluate the following improper integral whenever it is convergent. Enter divergent if the integral is divergent.

Find the area of the region under the given curve over the indicated interval.

Evaluate the improper integral if it is convergent.

Evaluate the following improper integral whenever it is convergent. Enter divergent if the integral is divergent.

Evaluate the following improper integral whenever it is convergent. Enter divergent if the integral is divergent.