Trig integrals

**coolguy99** · April 16th 2009, 06:40 PM

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)

**e^(i*pi)** · April 16th 2009, 06:45 PM

Originally Posted by coolguy99

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)

Use the double angle formulae:

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

In this case $A = 2\theta$

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

In this case $A = 4\theta$

------------

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

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

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