## anonymous 2 years ago Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(s)= integral 2 to s (t-t^3)^5

1. anonymous

the derivative of the integral is the integrand replace $$t$$ by $$s$$ in the integrand and you are done

2. anonymous

this is much much easier than it seems

3. anonymous

The fundamental theorem basically says that when you have an integral going from a number to some variable, we substitute that variable for the inside and multiply by it's derivative.

4. anonymous

In this case the derivative of s is just 1 so we can disregard that.

5. anonymous

for example, the derivative of $\int_2^x\frac{t^2+2}{t-1}dt$ is $=\frac{x^2+2}{x-1}$

6. anonymous

^ Yeah that's good.

7. anonymous

thanks...d

8. anonymous

No problem :) .