Question

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

Answer 1

the derivative of the integral is the integrand
replace \(t\) by \(s\) in the integrand and you are done

Answer 2

this is much much easier than it seems

Answer 3

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.

Answer 4

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

Answer 5

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

Answer 6

^ Yeah that's good.

Answer 7

thanks...d

Answer 8

No problem :) .