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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 ...
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 ...

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x)= \int\limits_{0}^{t} 4 \sin (x^3) dx\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Looks like they want you to use fundamental theorem of calculus part 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would 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?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Kind of all you have to do here is plug in t where x is

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ahhh thats what I did wrong

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1So we have \[\int\limits_{0}^{t} 4 \sin(x^3) dx = 4\sin(t^4)=f'(x)\]eas right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0had something like d/dx f[t] = f'[x]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Sort of haha, basically taking the derivative of integral, which just cancels out the integral, if that makes sense

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1It'll be rare for you to see fundamental theorem of calc part 1 after calc 1 xD

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1But part 2 what you did first is everywhere
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