Can someone just explain to me how these integrals work? I don't remember the identities well enough to do these haha..

integral of cos^2(2theta)

integral of sin^2(4theta)

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- Apr 16th 2009, 06:40 PMcoolguy99Trig integrals
Can someone just explain to me how these integrals work? I don't remember the identities well enough to do these haha..

integral of cos^2(2theta)

integral of sin^2(4theta) - Apr 16th 2009, 06:45 PMe^(i*pi)
Use the double angle formulae:

$\displaystyle cos(2A) = 2cos^2(A) - 1$ ---> $\displaystyle cos^2(A) = \frac{cos(2A) + 1}{2}$

In this case $\displaystyle A = 2\theta$

$\displaystyle cos(2A) = 1-2sin^2(A)$ -------> $\displaystyle \frac{1-cos(2A)}{2}$

In this case $\displaystyle A = 4\theta$

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Also $\displaystyle \int sin(Ax)dx = -\frac{1}{A}cos(Ax) + C$

$\displaystyle \int cos(Ax)dx = \frac{1}{A}sin(Ax) + C$