00:01
Given f of x comma y is equal to c of y square minus x square multiplied by e power minus y, where x varies from minus y to plus y and y varies from 0 to infinity.
00:23
So first we are going to calculate the value of c, that is double integral minus infinity to infinity, x comma y, d x, dy is equal to 1.
00:38
Now applying the corresponding values, it will be in terms of integral minus infinity to infinity, sorry, 0 to infinity.
00:47
Then it will be minus y to y.
00:51
C multiplied by x square minus y square, sorry, y square minus x square, multiplied by e power minus x squared, multiplied by e power minus y, multiplied by d, multiplied by d, x, dy is equal to 1.
01:07
So first integrating the inner most part, it will be c, multiplied by integral over 0 to infinity, in terms of integral minus y to y, y square minus x square, multiplied by e power minus y, d x, multiplied by d, y, is equal to y.
01:36
On solving this, integrating the innermost part, we will be obtaining the solution to be 2y cube, e power minus y, minus 2 y, 2, ype, e power minus y, divided by 3, which is equal to.
01:56
So on simplifying further, we will be obtaining 4c3 multiplied by integral 0 to infinity, y cube, e power minus 1 .5.
02:10
Multiplied by d .y is equal to 1...