Wallis's formula question:

Question

anonymous · Answer

$$\int\limits_{0}^{pi/2}\cos^4\theta d \theta$$

anonymous · Answer

i have the formula infront of me, but i am alittle confused as how to apply it, in my book they applied the formula and found this integral to be :3pi/16

anonymous · Answer

oh i just figured it out, wallis formula goes like this:
If n is even (n greater than or equal to 2), then:

$$\int\limits_{0}^{pi/2}\cos^n \theta d \theta$$=(1/2)(3/4)(5/6).....((n-1)/(n))(pi/2)

anonymous · Answer

now 1/2 corrspond to n=2, and then from then (1/2) time(3/4) corresponds to n=4, (since n has to be even)

anonymous · Answer

thus for my integral i have (1/2)(3/4)(pi/2)=3theta/8

anonymous · Answer

nice and easy way to integrate these sin and cos functions with even powers

beginnersmind · Answer

Nice, haven't seen it before. Reading the wikipedia article now. Seems like it's more important theoretically, as the integral itself isn't too hard.

anonymous · Answer

yeah, sure, but when your taking a test and your time is running low, its good to have this in your arsenal

beginnersmind · Answer

Hm, I guess it could come up often when you're trying to calculate Fourier series.