What trig identity did they use?

quickclick330 · Jan 31, 2008

Hi I'm having trouble understanding how they simplified this integration using trig substitutions...I really don't know what identities they used to make these substitutions or the strategy behind why this substitution was made(particularly the 3 steps in the red box). Obviously it works but I just can't click into place why...thanks for the help!

Handwritten-style worked integral: integral from 0 to pi/2 of sin^2 x cos^2 x dx, rewritten as 1/4 times integral of 4 sin^2 x cos^2 x, then 1/4 times integral of (2 sin x cos x)^2, then 1/4 times integral of sin^2 2x, with the middle steps boxed in red.

ircdan · Jan 31, 2008

double angle formula, sin(2x) = 2sinxcosx

What trig identity did they use?

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