# Total Revenue

1. May 3, 2012

### jodd8782

1. The problem statement, all variables and given/known data
According to data, the marginal revenue of a product(in billions of dollars per year) is approximated by 3.96+.01x+.0012x^2, where x=0 corresponds to 1980. What was the total revenue from the beginning of 1996 through the end of 2002?

2. Relevant equations

3. The attempt at a solution
∫23 on top, 17 on bottom (3.96+.01x+.012^2)=(3.96.02x^2+.004x^3)|23 on top, 17 on bottom
63.208-29.392=33.816

2. May 3, 2012

### Staff: Mentor

Do you have a question?

3. May 3, 2012

### jodd8782

yes the answer i got 33.816 was wrong, can you help with the solution

4. May 3, 2012

### Staff: Mentor

The beginning of 1996 corresponds with x = 16, not 17. The other limit of integration, 23, looks OK.

$$\int cx^n dx = \frac{c}{n+1}x^{n+1}$$
I omitted the constant of integration since you're working with a definite integral.
What you're doing looks like you are differentiating, not integrating.

5. May 3, 2012

### jodd8782

ok im still confused

6. May 3, 2012

7. May 3, 2012

### Staff: Mentor

For the integration part, the integrand is 3.96+.01x+.012^2 (the last term should be .012x^2).

The antiderivative you showed is 3.96.02x^2+.004x^3.

1. In the antiderivative you have two terms munged together (3.96.02x^2).
2. The antiderivative of 3.96 is NOT 3.96.
3. The antiderivative of .01x is NOT .02x^2.