integrate sqrt(1-x^2-y^2)dy

Question

ganeshie8 · Answer

that looks like part of double integral ?

anonymous · Answer

yup

anonymous · Answer

$$\int\limits_{-1}^{1}\int\limits_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int\limits_{0}^{\sqrt{1-x^2-y^2}}dzdydx$$

ganeshie8 · Answer

$\large z = 1-y^2$ is not a cylinder

ganeshie8 · Answer

I don't see how that triple integral represents the region in first octant bounded by the given planes... could u check once ? :)

anonymous · Answer

ganeshie8 · Answer

its a sphere !

ganeshie8 · Answer

you're working question sixteen b, or sixteen a ?

anonymous · Answer

oh i am sorry i am working for hours.its my mistake i posted wrong question

anonymous · Answer

b

ganeshie8 · Answer

equation of sphere of radius $1$ and centered at origin : 

$\large x^2 + y^2 + z^2 = 1$

ganeshie8 · Answer

$\large   z^2  = 1-x^2 - y^2$

$\large   z  = \pm \sqrt{1-x^2 - y^2}$

ganeshie8 · Answer

Upper hemi-sphere :
$\large   z  = + \sqrt{1-x^2 - y^2}$

Lower hemi-sphere :
$\large   z  = - \sqrt{1-x^2 - y^2}$

ganeshie8 · Answer

The question is asking u to just setup the triple integral for volume of upper sphere

ganeshie8 · Answer

|dw:1402049968912:dw|

ganeshie8 · Answer

can u sketch the hemisphere ^