1. ## Integration help

suppose , find f'(Pi^(1/3))

Im not sure weather i integrate or diffrenciate.

2. Originally Posted by geurrp the yard
suppose , find f'(Pi^(1/3))

Im not sure weather i integrate or diffrenciate.
This is an application of the chain rule. Say that $F(y)=\int\sin(5y)\,dy$. Thus, we are given that $f(t)=F(-t^3)-F(3)$.

Now take the derivative. (Remember, $F(3)$ is a constant, so its derivative is $0$.)

$f'(t)=\underbrace{F'(-t^3)=\sin(5\cdot-t^3)\cdot\frac{d}{dt}[-t^3]}_{chain~rule}=\sin(-5t^3)\cdot-3t^2=\boxed{3t^2\sin(5t^3)}$

(Recall that sine is an odd function so $\sin(-5t^3)=-\sin(5t^3)$.)

3. Hi, Why dont you integrate that sin5y function?

4. You could if you wanted to, but it would be unnecessary work as you would be differentiating again immediately. Also, don't forget to plug $\sqrt[3]{\pi}$ into the boxed equation.

5. Im just a little confused, when I see a integral sign, I automaticaaly assume to integrate. Also why did you not find the derviative of sin?

6. $\frac{d}{dx}\left[\int f(x)\,dx\right]=f(x)$

You don't need to integrate and differentiate to know that's true.

7. Hi when i sub in cube root of Pi into the equation I get zero. Because sin5(pi)Is that correct?

8. Yes I agree