00:01
So we have the picture here to the left that represents our function and we want to find three integrals.
00:05
So let's go ahead and first find the interval from 0 to 3.
00:09
So that is going to represent this area here in red.
00:13
So because that's a triangle we're going to use the equation for the area of a triangle, which is 1 half base times height.
00:19
So our base here is going to be 3 because that's the horizontal distance here.
00:24
So we're gonna have 1 half times 3 and then our height is going to be from 0 to 4 here, which tells us our height is 4.
00:33
So multiplying this out we get the integral from 0 to 3 is then going to be 6.
00:41
Next we want to find the integral from 3 to 5.
00:45
So the integral from 3 to 5 is then going to be this blue region here.
00:53
Now notice that this is actually going to equal 0 because the integral from 3 to 4 here has a base of 1 in a height of 4 and then the integral from 4 to 5 has a base of 1 in a height of negative 4...