Question

is there an easy way to integrate sin^2xcos^2x dx

Answer 1

sin^2 (2x)/4

Answer 2

nope..

Answer 3

First:
rewrite Cos^2 as (1-Cos^2x)

Answer 4

Sorry lagging meant (1-Sin^2x)
then ull end up with
Sin^2x-Sin^4x dx

Answer 5

ok

Answer 6

then use the power reduction formulas.. something like Sin^m where m is odd, etc..
actually here's the link:
http://www.wolframalpha.com/input/?i=integrate+%28Sin%5E2xCos%5E2x%2Cx%29
im too lazy to type this out, sorry just click on show steps.

Answer 7

i was looking at that.. i ask for a simple way to look for the answer

Answer 8

Anilorap: Unfortunately I don't think there is a easy way for the trig functions outside of their power reducing formulas. The only way this could be nicer is if u-substitution worked... which because the cosine is squared, makes it not an option. The only way for this to appear simple is if you've do a bunch of them over and over and get the hang of seeing the formula. No cut to the chase here.

Answer 9

use euler formula to convert sin's and cos's to exponents then its a piece of cake

Answer 10

thanks.. oreo... i think u r right

Answer 11

Evern also has a really good point. But if you don't work with complex numbers Eulers is kind of scary to see for the first time. I actually have never done it with the Euler's version. I bet it would be quite fun to work it out that way.

Check them out if you're interested. I wouldn't scare yourself over them if all you're working on is Calc 1-3 or the basic calculus sequence. But if you're an engineer/physicists/math major go here: http://planetmath.org/encyclopedia/ComplexSineAndCosine.html

Answer 12

forget power reduction formulas...

sin^2(x)*cos^2(x) = (sinx*cosx)^2 = (1/2*sin(2x))^2

= 1/4*sin^2(2x)

= 1/4(1 - cos(4x))/2

= 1/8(1 - cos(4x))

integrating this is easy:

1/8(x - 1/4*sin(4x)) + C