The problem is d/dx int sin(t) from x^2 to x^3, am I allowed to separate the problem up like d/dx int sin(t) from 0 to x^3 and d/dx int sin(t) from x^2 to 0 ?

Question

The problem is d/dx int sin(t) from x^2 to x^3,  am I allowed to separate the problem up like   d/dx int sin(t) from 0 to x^3 and d/dx int sin(t) from x^2 to 0 ?

owlfred · Answer

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

anonymous · Answer

theres a simple rule

anonymous · Answer

3x^2 sin(x^3) - 2x sin(x^2)

anonymous · Answer

So I am allowed to separate the two functions?

anonymous · Answer

no its like this

anonymous · Answer

let any integral of f(t) from function of x g(x) to function h(x) be r(x)

anonymous · Answer

then r'(x) is h'(x)f(h(x)) - g'(x)f(g(x))

amistre64 · Answer

$$\frac{d}{dx}\left( \int_{x^2}^{x^3} sin(t)\right)$$
this?

anonymous · Answer

Yes

anonymous · Answer

yes

amistre64 · Answer

im sure theres a fundamental thrm at work here....

anonymous · Answer

i proved it once amistre..u were there too

amistre64 · Answer

lol.... but that was sooo long ago :)

anonymous · Answer

it was indeed

anonymous · Answer

Thanks folks.

anonymous · Answer

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