Question

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

Answer 1

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

Answer 2

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

Answer 3

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?

Answer 4

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

Answer 5

ahhh thats what I did wrong

Answer 6

thnx

Answer 7

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

Answer 8

easy*

Answer 9

Np :-)

Answer 10

had something like

d/dx f[t] = f'[x]

Answer 11

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

Answer 12

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

Answer 13

But part 2 what you did first is everywhere