00:01
Thank you very.
00:02
So recall for this problem that the cosine of x is equal to the sound from 0 to infinity of negative 1 to the n power times x to the power of 2n divided by 2n factorial.
00:16
So that implies that cosine of the xbite is simply going to be the solve from n equals 0 to infinity of negative 1 to the n power times x to the power of 4n divided by 2n factorial.
00:28
What does that mean? it means that the integral of majority 2 of cosine of x squared d x is simply going to be the sum from n equals 0 to infinity of the integral of the integral to nth power times x of the power of 4n divided by 2 n d x and that this would equal to the sum from n equals 0 to infinity of negative 1 to the power of n times x the power of 4 n plus 1 divided by, well first of all 2 n total times 4 n plus 1 and then evaluating this from 0 2 will give us the sum from n equals 0 to infinity of negative 1 to the n power times 2 to the power to 4 n plus 1 divided by 2 n factorial times 4n plus 1 and when 0 0 we simply get 0 so let's start plugging in n equals 0 so if n equals 0 we're going to 2 to the power of 1 divided by if n equals 0 is just going to be 1 times 1 minus if n equals 1 we're going to get 2 to the power of so n equals 1 so 5 divided by 2 n factorial so here if n equals 1 we're going to get 2 factorial times of 5 plus 2 to the power of 5 plus 2 to the power of if n equals 2 it's going to be 9 divided by.
02:05
Here we're going to have 2 times 2, which is 4 factorial, times 9.
02:12
And then one more to get the 4th.
02:14
So it's going to get 2 to the power of.
02:16
So if n equals 3, 3 times 4 is 12 plus 1, it's 13th, divided by.
02:27
And here if n equals 3, we're going to be 6 factorial times 13th.
02:32
So this is what we're doing.
02:34
Pretty much we're using the first four terms of the clorin series...