00:01
So when you look at this problem, you have y equals x squared, and you'll also have y equals 4.
00:14
And what we need to examine is this region in here.
00:18
And the first thing that they ask you to do is find that the area or volume, when you take that and you do the squares, which would be your upper function of 4 minus the lower function of x squared, in terms of x and i don't know if it's as obvious that the bounds are going to be from negative two to two because if you set those two equations equal to each other all you have to do is square root both sides and you can see that they would intersect at posom in negative two so what i would do is uh i would actually foil this out you know four times four then the outside of be negative four x squared the inside is negative four x squared to give me negative of 8x squared and then plus x to the fourth power d x.
01:10
So at this point, you can evaluate the integral, adding 1 to the exponent, multiply them by the reciprocal of your new exponent.
01:20
Now we're doing this from negative 2 to 2.
01:23
And i've already done this, plugging in 2 and for all these bounds, plugging negative 2 and for all those bounds, you get exactly 512 .15th.
01:35
So that's your answer to part a where you have squares.
01:40
And the difference with semi -circles is, you know, draw this in blue, is it looks something like this.
01:51
So there's a formula out there for part b where most of the equation is the same...