00:01
So we have this problem today on definite integrals.
00:04
We are given this function.
00:14
It's on multivariate calculus.
00:16
F, xy equals root over of x plus root over of y to integrate double integral 0 to 1 to 1.
00:44
This function root over of x plus root over of y, dx, d.
00:54
So let us solve this.
01:00
We can write the integral as i equals 0 to 2, 0 to 1, root over of x plus root over of y over dx, y over dx, this equals 0 to 2, 0 to 1, root over x over d x, dy, d .y plus 0 to 1, 0 to 2, root over of y, d .y, dx.
02:09
Now we can change the order of integration from dx to dy dx because the function root over x and root over y, both are continuous in the range 0 to 1 and 0 to 2 respectively.
02:24
So we can interchange the order of integration.
02:27
So there is what we have done.
02:33
So this, if we compute, this will be 0 to 2.
02:41
If we integrate root over x over dx, then this becomes 2 over 3 times x to the power 3 by 2.
02:59
And this whole thing has to be computed within the range 0 to 1.
03:07
And that has to integrate it over d .y.
03:15
And this one, we can write 0 to 1.
03:22
And this thing again will be 2 over 3 y to the power 3 over 2...