I'm a bit confused about the average equations with integration. I need to solve this problem, and I think I'm supposed to use substitution, but I can't get it to work. The problem looks like this:

Question

z(t)=4tsin(t^2), [0,π^1/2]

Any input?

Answer 1

Let
u=t^2
du = 2tdt
∫z(t)dt
=∫4tsin(t^2)dt from 0 to sqrt(π)
=∫2sin(u)du from 0 to π
=-2cos(u) from 0 to π
=-2[-1 - (1)]
=4