Question

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

Answer 1

`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`.