00:01
Hi, in this question we need to find the surface area.
00:04
We know that the formula to find surface area equals integral 2 pi x into d s.
00:13
This is rotation about y axis, where ds equals square root of 1 plus d x by dy, the whole square into dy.
00:33
Here, given graph is y equals 4 minus x squared and y equal to 0 about the y axis.
00:49
First we need to find x.
00:51
So here x squared can be written as 4 minus y.
00:56
X equals square root of 4 minus y.
01:00
D differentiating with respect to y, then we get d x by d .y equals 1 by 2, 4 minus 2.
01:07
The whole power minus 1 by 2 into minus 1 which is equal to minus 1 divided by 2 square root of 4 minus y which can be written as minus 1 by 2 x.
01:27
Here surface area can be written as integral 2 pi x into square root of 1 plus dy x the whole square that is minus 1 by 2x the whole squared into d .y, which is equal to integral 2 .5x into square root of 1 plus 1 by 4x squared into d .y...