Homework 4.1

1. Evaluate the following indefinite integral.

$\int x^{7}dx$

2. Evaluate

$\int \frac{1}{x^3}dx$

3. Evaluate

$\int \sqrt{x^{11}}dx$

4  Determine the indefinite integral below.

$\int \frac{dx}{x^5}$

5.  Evaluate. Assume that x>0

$\int \left(\frac{10}{x}–\frac{3}{x^2}\right) dx$

6.  Evaluate

$\int e^{5x}dx$

7. Determine the following.

$\int 5 e^{–4x}dx$

8.   Determine the indefinite integral below.

$\int \left(\frac{7}{x}–5 e^{3x}+\sqrt{x^7}\right) dx$

9.  Find f such that

10.  Find f such that

11. A company determined that the marginal​ cost, 

of producing the xth unit of a product is given by

Find the total cost function​ C, assuming that​ C(x) is in dollars and that fixed costs are ​$4000

.C(x) =

12. A company selling parachutes determines that the marginal​ revenue, R’ ​, in dollars per​ unit, from selling the xth parachute is given by

​a) Find the​ total-revenue function,​ R, assuming that R(0) = 0
.
​b) Why is R(0) = 0 a reasonable​ assumption?

13. Evaluate. The answer can be determined by rules of​ antidifferentiation, but some algebra may be required beforehand.

14.  Evaluate. The answer can be determined by rules of​ antidifferentiation, but some algebra may be required beforehand.