Question

Use part 1 of the Fundamental Thm of Calc to find the derivative

g(s)=integral from 5 to s of (t-t^2)^8 dt

Answer 1

If f(t) = (t-t^2)^8, and g(s)=integral from (any number) to s of f(t), then g'(s)=f(s)=(t-t^2))^8.

Basically, the s jumps in, replaces the t's and the integral sign goes away.

If it was integral from 5 to s^2, for example, the s^2 would still jump in and replace the t's, but you'd also have to multiply by the derivative of s^2 (2x)

Answer 2

so its.. (s-s^2)^8?

Answer 3

yes :)

Answer 4

ohhhh I meant to write it as g'(s)=f(s)=(s-s^2))^8. Sorry!

Answer 5

it's okay (: thank you!