Use substitution to evaluate the definite integral. The integral from 0 to pi/3 of sinxcos x dx.

2. Originally Posted by juicysharpie

Use substitution to evaluate the definite integral. The integral from 0 to pi/3 of sinxcos x dx.
$\int_0^{\frac \pi3}\sin(x) \cdot \cos(x) dx$

Let $u = \sin(x)$

Then $\dfrac{du}{dx} = \cos(x)~\implies~du=\cos(x) dx$

Since $\sin(0)=0$ and $\sin\left(\frac \pi3\right)= \frac12 \sqrt{3}$ the integral becomes:

$\int_0^{\frac \pi3}\sin(x) \cdot \cos(x) dx~\implies~\int_0^{\frac12 \sqrt{3}}udu =\left. \frac12 u^2\right|_0^{\frac12 \sqrt{3}}$