Calculus
posted by Rachel .
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:
z(t)=4tsin(t^2), [0,π^1/2]
Any input?

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