00:03
In this question, we're asked to find the area between these two curves.
00:11
It's shaded in blue.
00:16
Now, since we're not given any intersection points, the first thing we need to do is to find them.
00:22
And we can do this by just equating the two curves to each other.
00:31
So we'll have that sine x equals 2x over pi.
00:39
Now, how do we take care of this? how can we figure out where these two will intersect? well, the easiest way to do it is to just plug in values, plug in values for the sign that we think will be necessary.
01:02
So i think that x equals 0 will work, because if i put in 0, we'll get that we have the sign of pi or 2, we'll have the sign of 0, which is 0, equaling 2 times 0, which is 0.
01:17
So that's a good point.
01:18
The other point i'm suspicious about is pi over 2.
01:25
If i put in pi over 2, the sign of pi over 2, we know is 1, and we know that that's going to be equal to 2 over pi times pi over 2, which is just 1.
01:36
So that works.
01:38
So those are our two intersection points.
01:42
Now the next thing we need to do is we need to figure out which is on top and which is on bottom.
01:51
And from the graph, it's clear...