00:01
You probably don't have to draw this graph, but i'll go ahead and do that real quick, is we have a very narrow graph of y equals 4 minus 4x squared, shifted up 4.
00:15
It's downwards parabola.
00:18
And we are enclosed between that region and the x -axis.
00:26
So our triangles are going to be from right here.
00:30
I'm trying to draw it kind of nice.
00:31
So this triangle is going to be a lot larger, because, well, from the x -axis to that point on the curve, it's a lot larger, at least a lot larger than this one.
00:43
And when they say isosceles, then two of the sides are congruent.
00:49
And the height is equal to the base.
00:51
So i'm interpreting the base to be these side lengths.
00:54
And so if i just redrew that as an isosceles triangle with the height equal to the base, base being over here, well, the area of a triangle is always 1 half base times height.
01:13
And since the height equals the base, we can just write it like this.
01:16
So the volume that they're asking for, it'll be 1 half the integral of the base, which is actually just the equation for minus 4x squared squared in terms of x.
01:31
One more thing i guess i should have clarified is that these two x -intercepts, if i had set the equation equal to 0, would have been negative 1 and positive 1.
01:40
And i should show that work real quick.
01:42
Set it equal to 0.
01:43
So you could add 4x squared to the right side, divide 4 over.
01:50
So x squared equals 1, and square root that, and you'll get positive negative 1.
01:56
And so those are your two bounds that you have to do...