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Find ∫from .6 to 0 x^2/ sqrt(9-25x^2) dx

My teacher worked this on the board a little confused

O obviously the trig sub is asintheta. But it isn't in the right form yet. So get it there you pull out a 25 --) sqrt(25(9/25) - x^2 ) 5sqrt((9/25)-x^2 so x= (3/5) sintheta so dx = 3/5costheta. so you change the bounds pi/2 to 0

When you replace everything you get

∫pi/2 to 0 (9/25) times ( sin^2θ/ 3cosθ) times (3/5) cosdθ

Where does that (9/25) come from?

I understand how to do the rest, just totally confused where that constant comes

My teacher worked this on the board a little confused

O obviously the trig sub is asintheta. But it isn't in the right form yet. So get it there you pull out a 25 --) sqrt(25(9/25) - x^2 ) 5sqrt((9/25)-x^2 so x= (3/5) sintheta so dx = 3/5costheta. so you change the bounds pi/2 to 0

When you replace everything you get

∫pi/2 to 0 (9/25) times ( sin^2θ/ 3cosθ) times (3/5) cosdθ

Where does that (9/25) come from?

I understand how to do the rest, just totally confused where that constant comes

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