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KLscilevothma
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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.
Q1) Prove the following inequality:
1 < [inte]pi/20 (sin x)/x dx < (pi/2)
Q2) Show that for x > 0,
ex-1 <= [inte]x0 (e2t+1)1/2 dt <= 21/2(ex-1)
Q3) Let F(x) = [inte]2x0 et/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
Q1) Prove the following inequality:
1 < [inte]pi/20 (sin x)/x dx < (pi/2)
Q2) Show that for x > 0,
ex-1 <= [inte]x0 (e2t+1)1/2 dt <= 21/2(ex-1)
Q3) Let F(x) = [inte]2x0 et/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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