00:01
In the given question, we have to compute the volume of solid, the volume of solid which is bounded by, which is bounded by the surface, which is bounded by the surface, which is given as, given as z is equals to y square plus one, z is equal to 3 minus x.
00:30
If we substitute your z is equal to 3 minus x minus 1 is equal to y square, we get 2 minus x is equal to y square.
00:40
Therefore we have y is equal to plus minus under root 2 minus x and we have x is equal to negative 1.
00:50
Therefore we get the volume v is equal to integral from negative 1 to 2, integral from negative 1 to 2, integral from negative 1, to 2, then integral from negative under root 2 minus x to under root 2 minus x, then we have the third integral is y squared plus 1 to 3 minus x with d z, d y, x, sorry, with respect to x.
01:21
Now integrating, integrating, we get, because we will integrate the value of y square, plus 1 to 3 minus x with respect to z so we get z from y square plus 1 to 3 minus x which is equals to 3 minus x minus y square minus 1 so this gives us 2 minus x minus y square here also we have 2 minus x of 2 minus x minus y square with respect to y...