$I = \int_0^{\pi/2} \frac{\sin x}{\sin x + \cos x} dx$
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The question is asking for the derivative of 1/2 sin x. Show more…
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(a) Find sin x cos x dx using the substitution u = sin x. (b) Find sin x cos x dx using the substitution u = cos x. (c) Show that the two results are equal. (a) integral sin x cos x dx = (b) integral sin x cos x dx = (c) Substitute sin^2 x = 1 - cos^2 x into your answer for (a) and simplify.
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