00:01
This question, we have to find the area of the shaded region enclosed by the following functions.
00:05
Okay.
00:06
So what we can do is we can find first this particular area which has been enclosed by the red function and the y -axis so that it gives us this complete area.
00:15
Then we can subtract from this area, the area which is enclosed by the blue one and the same y -axis about y -equal to 4.
00:24
And if we subtract, then we'll definitely get the yellow region.
00:26
So what we have to do is we have to write x in terms of y, of course.
00:30
We have to integrate.
00:32
So x from here comes out as y over two and from here x square is 9y, which means that the value of x will come out as root of 9y.
00:41
I know it should be plus and minus, but since we are dealing only with the positive values of x, that's why i say that it's only positive, which can be written as 3 root y.
00:50
So if we have to set up the integral, that will, we just have to set up the integral, i think.
00:56
So if you have to set up the integral, then the area of the yellow region would be the area of the red one, which is 3 root y, or dy within the limits of 0 to 4, of course, 0 to 4, minus the area of the view one, which is y over 2, dy within the limits of 0 to 4 once again.
01:18
So this can be condensed to be written as 0 to 4, 3 root y minus y over 2dy...