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I have posted a link there to this thread so the OP can view my work.Derivative of integral?

F(x) = integral of e^(t^2)dt (upper limit = cosx, lower limit = sinx)

Now find F'(x) at x=0

HOW DO I SOLVE THIS :O

Okay so this is what I did,

solve integration, answer is [e^(t^2)]/2t

[2t is the derivative of power(t^2), you're suppose to DIVIDE the integration by the derivative, riiight?]

I put t=cosx, t=sinx

So, it becomes

e^({cosx}^2)]/2cosx - e^({sinx}^2)]/2cosx

Now I take its derivative...

which turns out to be very complicated so I think I'm doing it wrong, cuz it is supposed to be not-so-long.

THIS IS THE ANSWER GIVEN AT THE BACK:

Answer:

F ′(x)=exp (cos2 (x)) ·−sin (x)−exp (sin2 (x)) · cos (x) by FTOC

F ′(0)=exp (1) · 0−exp (0) · 1=−1

NOW HOLD ON A SECOND.

ISNT DERIVATIVE OF AN INTEGRAL, THE FUNCTION ITSELF? YESSSS.

OKAY, BUT THE DERIVATIVE AND INTEGRAL DONT UMMM CANCEL OUT TILL THE dx/dy/dt IS SAME WITH DERIVATIVE AND INTEGRATION!

Okay, I somehow solved the question B) *pat pat*

Can someone tell me how do i write this down on my paper??