Emineyy Group Title 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 11 months ago 11 months ago

1. satellite73 Group Title

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

2. satellite73 Group Title

this is much much easier than it seems

3. Dido525 Group Title

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 Group Title

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

5. satellite73 Group Title

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

6. Dido525 Group Title

^ Yeah that's good.

7. Emineyy Group Title

thanks...d

8. Dido525 Group Title

No problem :) .