Question

how to find the area between x-axis and g(x) from x=0 to x=pi
g(x) = xcos(x/2)

Answer 1

\[A = \int\limits_{0}^{\pi}x \cos(x/2) dx\]
u = x/2
du = 1/2 dx
\[=4\int\limits_{0}^{\pi}u \cos(u) du\]
then use integration by parts
u = u dv = cos u
du = du v = sin u