Hi again

I have another trig function so not sure what I am doing

using the V= (definite integral "S" a b) 2pi x f(x) dx formula

V = 2pi S a = 0; b=pi^1/2 sin (x^2) dx

then I am not sure what sin (x^2) dx becomes - is it = -(1/3)cos(x^3)???

I feel very confused

Thanks

Calculus beginner