## anonymous one year ago If f[x] = Integrate]t/0 4 Sin[x^3] what does it mean to 'give a clean formula' for f'[x] ? latex coming ...

1. anonymous

$f(x)= \int\limits_{0}^{t} 4 \sin (x^3) dx$

2. Astrophysics

Looks like they want you to use fundamental theorem of calculus part 1

3. anonymous

would that not just be $\int\limits_{0}^{t} f'(x) = f(t) - f(0)$ and there for f'(x) = 4 sin (x^3) Or is there more to it than that?

4. Astrophysics

Kind of all you have to do here is plug in t where x is

5. anonymous

ahhh thats what I did wrong

6. anonymous

thnx

7. Astrophysics

So we have $\int\limits_{0}^{t} 4 \sin(x^3) dx = 4\sin(t^4)=f'(x)$eas right

8. Astrophysics

easy*

9. Astrophysics

Np :-)

10. anonymous

had something like d/dx f[t] = f'[x]

11. Astrophysics

Sort of haha, basically taking the derivative of integral, which just cancels out the integral, if that makes sense

12. Astrophysics

It'll be rare for you to see fundamental theorem of calc part 1 after calc 1 xD

13. Astrophysics

But part 2 what you did first is everywhere