Question

Evaluate

∫
π
−
π
cos
2
(
5
x
)
d
x
.

Answer 1

`_( - \pi) \int ^(\pi) \cos(2(5x) dx = _( - \pi) \int ^(\pi) \cos(10x) dx \\ let \: 10x \: be \: u \\ (d(10x))/(dx) = du \\ dx = (du)/(10) \\ignore \: limits \\ _( - \pi) \int ^(\pi) \cos(2(5x) dx = \int \cos(u) (du)/(10) \\ = (1)/(10) \sin(u) + c \\ substitute \: for \: u \\ = (1)/(10) \sin(10x) |^(\pi) _( - \pi) \\ = (1)/(10) (( \sin(10\pi) - ( \sin( -10 \pi) ) \\`