# area

• November 17th 2010, 07:20 AM
area
find the area bounded by y^(2/3)+x^(2/3)=a^(2/3) and co-ordinate axes.
• November 17th 2010, 07:33 AM
HallsofIvy
Quote:

find the area bounded by y^(2/3)+x^(2/3)=a^(2/3) and co-ordinate axes.

Do you mean the area in the first quadrant?

$y= (a^{2/3}- x^{2/3})^{3/2}$

I recommend the substitution $x= u^3$ to integrate that.
• November 17th 2010, 08:40 AM
TheEmptySet
Quote:

Use the parametrization $x=a\cos^3(t)$ and $y=a\sin^3(t)$ to complete the simple close.
$\frac{1}{4}\iint_DdA=-\frac{1}{4}\oint y\,dx=-a^2\int_{0}^{2\pi}\sin^3(t)(3\cos(t)\sin(t))dt=-\frac{3a^2}{4}\int_{0}^{2\pi}\sin^{4}(t)\cos(t)\,d t$