00:01
Hello students, to find the area between the curves y square minus 4x equals to 4 and 4x minus y equals to 16, we need to find the points of intersection and then set up the integral to compute the area.
00:19
So, we solve the system of equations to find the point of intersection.
00:25
Therefore, 4x minus 16 whole square minus 4x equals to 4.
00:34
This implies 16 x square minus 132 x plus 252 equals to 0.
00:44
This implies 4 x square minus 33 x plus 63 equals to 0.
00:52
This implies x equals to 33 plus minus square root of 33 whole square minus 4 into 4 into 63 divided by 2 into 4.
01:10
If we calculate this, we have 33 plus minus 9 by 8.
01:16
Therefore, so we have two values of x, x1 equals to 33 plus 9 by 8.
01:24
This is equals to 5 .25 and x2 equals to 33 minus 9 divided by 8.
01:33
This is equals to 3.
01:35
Now, we find the corresponding y values.
01:39
Therefore, for x1 equals to 5 .25, y equals to 5 and for x2 equals to 3, y equals to minus 4...