Emineyy 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. satellite73

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

2. satellite73

this is much much easier than it seems

3. Dido525

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. Dido525

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

5. satellite73

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

6. Dido525

^ Yeah that's good.

7. Emineyy

thanks...d

8. Dido525

No problem :) .