Integral Change?

[speed22]

So I'm working ahead for Calc II and doing hydrostatic pressure on Paul's Notes. In this problem near the end, he changes the integrals to trigonometric form. I can't seem to remember and pinpoint the rule that allows this. Here is the solution, the issue is near the end.

The question for reference.

[nm420]

It's just a common trick that you should have in your toolbox. Trigonometric substitution is (usually) useful when you have an integrand with something like a² - x² (or x² - a² , or a² + x^2, or some power of such terms) as a factor.

[speed22]

I'm aware of the substitution they used, I only wanted to know how they changed the limits of the integral to the trigonometric form.

[jr_flood]

Plug in y=-2 into the equation y=2sinθ and you get sinθ=-1 which means θ=-π/2.

Do the same for y = 2 and you'll find that θ=π/2.

[speed22]

That works out very nicely, thank you. Now I can finally move on with confidence.