00:01
For the given equation, we are given a graph and the curve are y is equal to 3x, y is equal to 2 by 3x and y is equal to 40 minus x square.
00:13
So now here one by one we will compare these two equations and these two equations then we will find the area induced by these two regions and then at the end we will add these two areas in order to calculate the total area.
00:26
So here comparing these two first equation 3x is equal to 40 minus x square, we can say that we have x equals to minus 20 by 3 comma x is equal to 6.
00:42
This value is not usable, we just leave this one because this cannot be negated.
00:48
Now y is equal to 2 by 3x equals to 40 minus x square.
00:53
So we have x is equal to 5 and x is equal to minus 8, minus 8 is not possible.
01:00
So x is equal to 5 and x is equal to 6.
01:04
So here for both the case, we can say that our another value of this will be x square minus 40 equals to 0 which implies x square equals to 40.
01:17
So x is equal to 2 times under root of 10.
01:23
Now further, here in our case we need to calculate the area induced by it.
01:28
So area a1 equals to integration over 0 to 5, 3x minus 2 by 3x.
01:35
So simplifying this we have 3x square upon 2 minus 2 by 3 times x square by 2...