00:03
The volume v can be calculated using the integral that is v is equal to integral value a, b 2 pi multiplied by x multiplied by fx dx where fx is the distance covered sorry between the curves y is equal to 5 minus x and y is equal to 25 subtracted from x square at a given x value and a, b is the interval over which the region is bounded.
01:32
So first let's find the intersection points of two curves that is 5 minus x is equal to 25 subtracted from x square.
01:41
Now rearrange to get a quadratic equation x square subtracted from x subtracted from 20 is equal to 0.
01:49
Then factor x subtracted from 5 x added to 4 is equal to 0.
01:55
Now we can solve for x we get to intersection point that is x is equal to 5 and x is equal to minus 4.
02:06
So since the region is enclosed by the curve interval of integration will be a, b is equal to minus 4, 5.
02:28
Now let's find fx which is difference between the curves at the given x value.
02:36
So fx is equal to 25 subtracted from x square subtracted from 5 subtracted from x is equal to 20 subtracted from x square added to x.
02:49
The volume integral becomes v that is volume is equal to integral value minus 4, 5 2 pi multiplied by x multiplied by 20 subtracted from x square added to x dx...