What is the integral of int sin(x)cos(x) from 0 to 2?

1 Answer
Jan 31, 2016

int_0^2 sin(x)cos(x) dx = sin^2(4)/4.

Explanation:

Note that sin(x)cos(x) = 1/2 sin(2x).

Using that, we evaluate the above integral as:

int_0^2 sin(x)cos(x) dx = int_0^2 1/2 sin(2x) dx

= [sin^2(2x)/4]_0^2

= sin^2(4)/4 - sin^2(0)/4

= sin^2(4)/4.