## anonymous one year ago Compute the integral.

1. anonymous

2. anonymous

use one of those "reduction formulas" unless you want to create if from scratch

3. anonymous

think the best bet is to start with $\int \sin^2(x)(1-\sin^2(x))dx$ then $\int \sin^2(x)dx-\int\sin^4(x)dx$

4. anonymous

first one is probably in you book use $\sin^2(x)=\frac{1}{2}(1-\cos(2x)$ second use the reduction formula on the back cover of your text

5. anonymous

|dw:1442885312886:dw|

6. anonymous

would this route be okay?

7. IrishBoy123

$$\large \sin^2 x \cos^2 x = (\sin x \cos x)^2 = \frac{1}{4} \sin^2 2x = \frac{1}{4} ( \frac{1-\cos4x}{2} )$$