Answer
$P = 37.5W$
Work Step by Step
Start by setting up the integral to solve for rms. We want rms current because it will give us the same average power.
$i_{rms} = \sqrt {100/ \pi * \int^{\pi}_0 sin^4 (t) *dt } $
Use a trig identity to simplify the sin term into terms of cosine with different frequencies.
Then integrate to get:
$i_{rms} = \sqrt {100/ \pi *(3*t/8 - \frac{1}{4}*sin(2x) + \frac{1}{32}*sin(4x)|^{\pi}_0 } $
$ i_{rms}= \sqrt {\frac{3*100}{8}} $
Now calculate power using $P = i^2 *R$
$P = (6.1237)^2 *1$
$P = 37.5W$
