# Math Help - Integrals

1. ## Integrals

The marginal cost of manufacturing x yards of a certain fabric is C'(x)=3-0.01x+0.000006x^2 ( in dollars per yard ). Find the increase in cost if the production level is raised from 500 yards to 5000 yards.

and

fnInt((x^3 +3 + 1/(x^2+1))dx)

2. Originally Posted by sw3etazngyrl
The marginal cost of manufacturing x yards of a certain fabric is C'(x)=3-0.01x+0.000006x^2 ( in dollars per yard ). Find the increase in cost if the production level is raised from 500 yards to 5000 yards.
I suppose for this one you want:

$\int_{500}^{5000} \left( 3 - 0.01x + 0.000006x^2 \right)dx$

that is not a hard function to integrate. just use the power rule. unless you should be calculating something else. the only place i encountered things like "marginal cost" and such was in a microeconomics class, and we never used calculus at all, so i'm not sure how to relate everything

and

fnInt((x^3 +3 + 1/(x^2+1))dx)
what do you mean "fnInt"?

3. fnInt means integral

4. Originally Posted by sw3etazngyrl
fnInt means integral
ok. again, most of this integral is simple, you use the power rule. but you also have to know something else.

Power Rule: $\int x^n dx = \frac {x^{n+1}}{n+ 1} + C$ for $n \neq -1$

Something else: $\int \frac {1}{x^2 + 1}dx = \arctan x + C$

So,

$\int \left(x^3 + 3 + \frac {1}{x^2 + 1} \right)dx = \frac {1}{4}x^4 + 3x + \arctan x + C$

Now, can you do the first?