00:02
For the integral i equal to integral x going from 0 to 2 and y going from integral square root x to 2 of 6 divided by y cube plus 1 dy by dx.
00:20
So now we find the integral after changing its order.
00:35
Now we have x going from 0 to 2 and the y going from square root x to 2.
00:44
So therefore we have the function like that since x going from 0 to x going from 0 to 4.
00:52
So x going from 0 to 4 so this is the line x equal to 4 and it is x equal to 0 and since y going from square root x to 2.
01:01
So this is say suppose this is y equal to 2 and this is the graph of square root.
01:08
So therefore now so this is the area for which we have to find the integral.
01:15
So now after changing the order of integration the order of integration integration.
01:27
So we take y going from 0 so this is the origin 0 comma 0 after changing the order of integration we have y goes between 0 to 2 and x goes between x goes between 0 to y square since we have y equal to square root x so it's equal to y square.
01:52
So that is that is x going from 0 to y square.
01:59
So the integral x going from 0 to 4 to integral y going from root x to 2 6 divided by y cube plus 1 into dy by dx equal to after changing its order.
02:13
So we have integral by going from 0 to 2 and x going from 0 to y square of 6 divided by y cube plus 1 into dx into dy...