Question

Find the integral of cos^2 x dx from 0 to 2pi.

Answer 1

hint: cos^2(x) = (1/2) (1 - cos(2x))

Answer 2

And do I take the integral of that? How?

Answer 3

opps *plus*

Answer 4

cos^2(x) = (1/2) (1 + cos(2x))

Answer 5

But how do you integrate that?

Answer 6

well, we know:$$\int\frac12(1+\cos2x)\ \mathrm{d}x=\frac12\int(1+\cos2x)\ \mathrm{d}x=\frac12\left(\int1\ \mathrm{d}x+\int\cos 2x\ \mathrm{d}x\right)$$

Answer 7

I trust you can simplify both of these simpler integrals! for the latter, think back to u-substitution

Answer 8

Thanks. I got it.