Question about where to start this trig substitution integral

[vande060]

Homework Statement

∫ x^2√(a^2 - x^2) dx evaluate integral from 0 to a

Homework Equations

The Attempt at a Solution

so i know the format of this problem requires the substitution of asinϑ -π/2 ≤ ϑ ≤ π/2 , but i don't know how to change the bounds of the integral after the substitution of ϑ. i just nedd help with this point the rest of the problem shouldn't be an issue

 

[mistermath]

You're substituting x = a sin (t) so plug your limits into x then solve for t.
Ex:
0 = a sin(t) -> 0 = sin(t) -> arcsin(0) = t -> t = 0.

for upper boundary plug in x = a you get:

a = a sin(t) -> 1 = sin(t) -> arcsin(1) = t -> pi/2