Help needed to solve derivative of integral with cosine function | Mathematics | Page 1

glacial marsh Mar 16, 2023, 4:24 PM

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I'm currently working on a calculus problem and I could use some help. The question is to find the value of $F^{\prime}(\sqrt{\pi})$ if $F(t)=\int_0^t \cos \left(x^2\right) d x$.

I'm not sure how to approach this problem since the function inside the integral involves the cosine function with an argument of $x^2$. I know that the derivative of an integral involves the function being integrated, but I'm not sure how to apply that here.

If anyone could provide some guidance on how to approach this problem or any relevant formulas that I should be using, it would be greatly appreciated. Thanks in advance!

dense jasperBOT Mar 16, 2023, 4:24 PM

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pliant heraldBOT Mar 16, 2023, 4:24 PM

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dgh

oak furnace Mar 16, 2023, 5:24 PM

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Recall the fundamental theorem of calculus $$\frac{d}{dt}\int_0^t f(x) dx = f(t)$$

pliant heraldBOT Mar 16, 2023, 5:24 PM

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GhostOfToyman

glacial marsh Mar 16, 2023, 6:01 PM

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oak furnace Recall the fundamental theorem of calculus $$\frac{d}{dt}\int_0^t f(x) dx = f(t)...

What dooes the t and x represent?

glacial marsh Mar 18, 2023, 12:49 AM

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@oak furnace Hey, do you have time?

oak furnace Mar 18, 2023, 1:00 AM

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Sorry, i was going to respond yesterday but it completely slipped my mind

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Give me a few hours since im at work rn

still hollow Mar 18, 2023, 1:56 AM

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glacial marsh What dooes the t and x represent?

they're variables

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the theorem is true for any x and any t (and any integrable function f)

turbid pier Mar 16, 2024, 9:23 AM

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.solved #help-22 message

#Help needed to solve derivative of integral with cosine function