00:01
In this question, we are asked to find the area of the region bounded by the two given parabolas.
00:06
The general formula for the area is the integral from a to b of f of x minus g of x dx, where f of x is the upper boundary of the region and g of x is the lower boundary.
00:27
Now, and a and b are the points of intersection of the two curves.
00:32
So let's first find a and b.
00:34
Let's find the intersection of 2x squared minus x squared and x squared.
00:40
We can rewrite this as 2x squared minus 2x equals 0.
00:45
We can factor out 2x and in parentheses we are going to get x minus 1 equals 0, which means that the points of intersection are x equals 0 and x equals 1.
00:59
So the region is running between 0 and 1.
01:02
Now we need to figure out what is the upper boundary and what is the lower boundary.
01:06
If you are too lazy and don't want to draw a picture, you can do that by picking any point on the interval between 0 and 1.
01:16
So, for example, you can take 1�, 1 half belongs to the interval from 0 to 1...