00:01
Hello, if the given curve f of xy is equals to x plus y and our given curve is defined as x square plus y square equals to four in the first quadrant to zero, zero two.
00:16
Integration of this function can be written as here.
00:21
Since we have to integrate this function here.
00:23
So first of all, x square plus y square equals to four is equation of circle here.
00:28
As we know that equation of circle centered at origin can be written as a x square plus y square equals to r square so radius of this circle is equal to two here so if this one is our x -axis here and this one is our y -axis here then our radius will be here this one is this point is two zero here and this point is zero here this one is x -axis this one is y -axis and this one is or reason here.
00:55
So we have to integrate this function between 0 to 2 to 0 here.
01:00
So between 0 to 2 here in the first quadrant, this one is our curve here.
01:06
So integration of this function between 0 to 0 to 0 to 0 to 0 here is x limit will be 0 to 0 to 0 here from between this to this here.
01:20
Similarly limit of why between 0 to 2 will be this here.
01:23
So integrate.
01:24
Of f xy between here x limit will also be between 0 to 2 and y limit also be 0 to 2 d x dyx and y here so by simplifying this we can write it as a integration between 0 to 2 integration between 0 to 2 x plus y d x d y here so first we different integrate with respect to y so integration between 0 to 2 integration between 0 to 2 x plus y of d y into d x x x x x x x x x of d y into here.
01:55
So by simplifying this, we can write it as a integration between 0 to 2...