Suppose in general that we have two functions(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

F(x)= \int_{0}^{cos x}e^{xt^2} dt

[/tex]

[tex]

G(x)= \int_{0}^{cos x}\(t^2e^{xt^2} dt

[/tex]

[tex]

H(x) = G(x) - F'(x)

[/tex]

Where, I need to prove that

[tex]

H(\frac{\pi}{4}) = e^\frac{\pi}{8}/\sqrt{2}

[/tex]

Okay, so far I have computed the integrals of both of these functions, where I am confused is when computing [tex] F'(x) [/tex] do I differentiate the integrand with respect to x only, and then simply subtract the two functions. Sorry for the edit, I left off the [tex] dt [/tex] for both integrals. Any help would be appreciated!!

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# Suppose in general a pair of functions

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