00:01
Now, as per the question, we are going to integrate it as, we will take x, y, z equals rho, theta and pi, where rho would be greater than and equal to zero, pi would range in between zero to pi strictly, and theta would range in between zero to two pi strictly.
00:24
Now, we will take x equals rho sine pi cos theta, y is equal to rho sine pi sine theta, and which will imply that x square plus y square plus z square equals rho square.
00:47
So on integrating that is the given function to us from zero to two, from zero to whole root of 4 minus x square, and from 4 minus x square minus y square to limit under root of 4 minus x square minus y square, 4 times 4 root of x square plus y square plus z square dz dy dx.
01:25
So, now, this is going to be, as we have taken, we will take z square equals 4 minus x square minus y square.
01:35
So, we get x square plus y square plus z square equals 4.
01:41
So, as this is equal to rho square, so rho square equals 4, so rho would be equal to under root of 4 that is 2.
01:49
Now, we have got the value of rho...