Question

How do you integrate `intsqrt(9-x^2)(-2x)dx`?

Answer 1

Let `u = 9 - x^2`. Then, by the power rule, `du = -2xdx` and `dx = (du)/(-2x)`.

`=intsqrt(u)(-2x) * (du)/(-2x)`

`=intsqrt(u)du`

`=u^(3/2) + C`

`=2/3(9 - x^2)^(3/2) + C`

Hopefully this helps!