Question

the intigral from 0 to pi/2 of (e^(2-cosx))sinx dx =?

Answer 1

Let u = 2-Cos(x)

Answer 2

du = Sinx dx

Answer 3

Integral is from 0 to pi/2 but now I said let u = 2-Cos(x), so:
Lower limit: u(o) = 2 - Cos(0) = 2 - 1 = 1

Answer 4

Upper limit: u(pi/2) = 2 - Cos(pi/2) = 2-0 = 2

Answer 5

So now you have:
Integral from 1 to 2 e^u * du = e^u (from 1 to 2)

Answer 6

e^2 - e = e(e-1)

Answer 7

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Answer 8

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Answer 9

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Answer 10

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Answer 11

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