00:01
Hello students in this question it is given that the function y is equal to x plus 2 and the other function is y equal to x squared and the density function is given as k x is 4 and we have to find in the first part of question the mass of body and in the second part of the question we have to find the coordinates of center of mark.
00:31
Let us draw the given curves.
00:34
Suppose this is the y axis and this is xxx.
00:41
This curve y is equal to x squared in a paraproly form.
00:48
The other function that is y is equal to x plus 2 is the straight line with interset 2.
00:56
So this this is the line y is equal to x plus 2.
01:02
This is called the y is equal to x square.
01:06
So first of all we will need to find the intersection point.
01:10
That is this point and this point so the given equation is y equal to x plus 2 and y is equal to x square so if we put the value of y as x squared in this equation you can get to x is 5 plus x x x plus 2 so we can write this as x x x minus 2 2 equal to 0 again we can write this as 2 x plus x minus 2 equal to 0 therefore we we can write this as x plus 1 equal to 0 so the value of x will be 2 and minus 1.
01:42
At x equal to minus 1, the value of y will be, if we put in any of the equation, that will be 1.
01:48
And at x equal to 2, the value of y will be x squared, that is 4.
01:54
So we can say that this point is minus 1.
01:58
So this coordinate of this point is minus 1, 1, and this point is to 4.
02:03
And this is the common area between both the curve.
02:09
Now, for the first part, we have 5...