## Evaluating a surface integral with parametric equations

Question is as follows:

Evaluate the Surface Integral.

$\int \int yz dS$

S is the surface with parametric equations x = u2, y = usin(5w), z = ucos(5w), 0 ≤ u ≤ 1, 0 ≤ wπ/(10).

I attempted it using the formula $\int \int f(r(u,w))*|r_u X r_v|dA$

This gave me \int \int (usin(5w)ucos(5w))*sqrt((-5u(sin(5w))^2 - 5u(cos(5w))^2)^2+(10usin(5w))^2+(10ucos(5w))^2)

(sorry was too long for image).

I then evaluated this with respect to the given limits and got (5^(3/2))/10which is incorrect.

Is there an easier way to do this or did I make a silly mistake somewhere?