00:01
Let's start the solution.
00:03
In this question we are given curve y is equal to x by 4, y is equal to 1 plus root x, y is equal to 2 root x.
00:16
Say this one is equation 1, this one is equation 2 and this one is equation 3.
00:21
It is necessary to find the intersection points of curve.
00:26
So now by equating equation 2 and 3 and simplify we get 1 plus root x equal to 2 by root x.
00:33
If we multiply root x, both members of the equality, we get here root x 1 plus root x equal to 2 by root x into root x.
00:45
This root root is cancelled out so we get root x plus this one is x equal to 2.
00:55
So we get here root x equal to 2 minus x by squaring both sides.
01:05
We get here x equal to 4 plus x square minus 4x.
01:13
So by simplifying this we get quadratic equation y is x square minus 5x plus 4 equal to 0 and roots of this quadratic equation or factor of this equation is x minus 1 x minus 4 equal to 0.
01:28
So we get x is 1 and x is equal to 4.
01:32
Say this one is x1, this one is x2.
01:35
Now by equating equation 1 and 3 and simplify we get x by 4 is equal to 2 by root x.
01:45
Now calculating the area of the left region.
01:50
So that is a1 is integration a to b f of x minus g of x dx...