More examples of integrals involving powers of trigonometric functions
Today's nonsense:
- New cheerleader poster
- Little Dokata missing again
- Megan's genetically diabetes
- Katie and bee stings: "glad that they sting and die"
Example #3 - integral of sin^{2}x cos^{5}x dx. What you have to do here is convert the integral into either the sine or cosine. The "u" variable can be either of them. So then the du will get rid of the other one. There is no lone sine or cosine, because there's one squared and the other to the fifth. The pythagorean identity tells us that we can change two sines at the same time or two cosines at the same time. So we can take the one that has an odd exponent (in this case, cosine), and if they each had odd exponents take either one, and then separate it.
= integral sin^{2}x * cos^{2}x * cos^{2}x * cosx dx
= integral of sin^{2}x * (1-sin^{2}x)cosxdx
u=sinx
du = cosxdx