Question

Integration using substitution trigonometric help me? int x/sqrt(9-x²) dx

Answer 1

`int x/sqrt(9-x²)dx=-sqrt(9-x^2)`

Explanation:

`int x/sqrt(9-x²)dx`

Let `x=3costheta`, then `dx=-3sinthetad theta`

and `intx/sqrt(9-x²)dx`

= `int(3costheta)/sqrt(9-9cos^2theta)*(-3sintheta)d theta`

= `int(3costheta)/(3sintheta)*(-3sintheta)d theta`

= `-3intcosthetad theta`

= `-3sintheta`

= `-sqrt(9-x^2)`