00:01
Here on this problem, we've been given the function y equals a into the negative 1, x.
00:07
And we're about to find first the area of the region bound by y equals 0, and x equals 1.
00:20
Now, if you plug in 1 there, we're going to get a into the negative 1 back.
00:26
And so that's where this point would be.
00:28
And so we're wanting the area of this region here.
00:32
That'd be a straight line.
00:36
Now you can use calculus if you want to, but you also.
00:38
Know that this base is one, this height is a end of the negative one.
00:43
That's a triangle.
00:45
That's just means that the area is one half base times height.
00:50
That's just one half the end of the negative one.
00:53
So that's the area of that region.
00:56
And you can use calculus and integrate it.
00:58
I just prefer to use the geometry there when possible.
01:03
Now on b, we're going to find the volume of the region by revolving in about the y -axis.
01:09
I was about to do the x -axis there...