solve the definite integral from 0 to pi/2 of cos^2(x)dx

Question

tkhunny · Answer

What's preventing you from solving it?

anonymous · Answer

i'm suppposed to evaluate it using the integral from 0to pi/2 of cosx dx being equal to the integral from 0 to pi/2 of sinx dx. I dont see how this relates to cos^2(x)dx

tkhunny · Answer

That's odd.  It's a lot easier if you let some trigonometry help you.

Think in this important identity:  $\cos(2x) = 2\cdot\cos^{2}(x) - 1$

Are we insisting that we use the given method?

anonymous · Answer

yeah because its a proof :(

tkhunny · Answer

You can integrate by parts, once, and prove the arguments $\cos^{2}(x)\;and\;\sin^{2}(x)$ produce identical results.

anonymous · Answer

ok, im gonna give it a try

tkhunny · Answer

Split it up cos(x) and cos(x).

anonymous · Answer

yeah I think i got it. thank you

tkhunny · Answer

Super!  Good work.

anonymous · Answer

i have to evaluate and i just evaluated them both to equal 1/2

tkhunny · Answer

??  It should be "1" with just cosine and pi/4 with cosine squared.

tkhunny · Answer

I'm still not sure how we used the hint.