I'm now teaching myself several topics on definite integrals for a math test on monday. Here are a few problems that I don't know how to do.(adsbygoogle = window.adsbygoogle || []).push({});

Q1) Prove the following inequality:

1 < [inte]^{pi/2}_{0}(sin x)/x dx < (pi/2)

Q2) Show that for x > 0,

e^{x}-1 <= [inte]^{x}_{0}(e^{2t}+1)^{1/2}dt <= 2^{1/2}(e^{x}-1)

Q3) Let F(x) = [inte]^{2x}_{0}e^{t/x}dt. Find F'(x)

Any help would be appreciated.

Edit: I know how to do Q3 now but I still don't understand why the upper limit can change to 2 after substituting u = t/x

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# Definite integrals

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