Question 344597
{{{9x^2-x^4=x^2(9-x^2)}}}
{{{sqrt(9x^2-x^4)=sqrt(x^2(9-x^2))}}}
{{{sqrt(9x^2-x^4)dx=x*sqrt(9-x^2)dx}}}
Let {{{u=9-x^2}}}
{{{du=-2x*dx}}}
{{{x*dx=-du/2}}}

{{{sqrt(9x^2-x^4)dx=sqrt(u)*(-du/2)}}}
{{{ int( sqrt(9x^2-x^4), dx )=int(-(1/2)sqrt(u),du) }}}
{{{ int( sqrt(9x^2-x^4), dx )=int(-(1/2)u^(1/2),du) }}}
{{{ int( sqrt(9x^2-x^4), dx )=-(1/2)(u^(3/2))/((3/2))+C }}}
{{{ int( sqrt(9x^2-x^4), dx )=-(1/3)u^(3/2)+C }}}
{{{ int( sqrt(9x^2-x^4), dx )=-(1/3)(9-x^2)^(3/2)+C }}}
{{{ int( sqrt(9x^2-x^4), dx,0,3 )=-(1/3)((9-3^2)^(3/2)-(9-0^2)^(3/2)) }}}
{{{ int( sqrt(9x^2-x^4), dx,0,3 )=-(1/3)(0-(9)^(3/2)) }}}
{{{ int( sqrt(9x^2-x^4), dx,0,3 )=-(1/3)(-27) }}}
{{{ int( sqrt(9x^2-x^4), dx,0,3 )=highlight(9) }}}