00:01
Hello students, to find the area of the array is unbounded by y equal to 8 by 4 plus x square and y equal to 1, we need to calculate the integral of the difference between the two functions over their common domain.
00:15
First, let's find x value where the two functions intersect.
00:18
So, y equal to 8 by 4 plus x square equal to y equal to 1.
00:24
So, 8 by 4 plus x square equal to 1.
00:28
So, 8 equal to 4 plus x square.
00:32
Now, we can write x square equal to 4.
00:35
So, x is equal to plus or minus 2.
00:38
So, the two functions intersect at x equal to minus 2 and x equal to 2.
00:46
Now, let's integral the difference between two functions over the interval that is minus 2 to 2.
00:52
So, a equal to integration from minus 2 to 2, 8 by 4 plus x square minus 1 into dx.
01:00
To evaluate the integral, we can use trigonometric substitution...