00:03
Hi, so in this question we're going to be solving for the integral.
00:07
So we have the integral of the signs of 5 theta squared d theta.
00:11
So the first thing we're going to do is we're going to use an equation that states that the cos of 2 theta is equal to 1 minus 2 sine squared theta.
00:32
And so we're going to have that our sine squared theta is equal to 1 minus the cos 2 theta over 2.
00:48
And so we're just going to plug this in and we're going to plug in our 5 times our 2 and we're just going to have 10.
00:55
So we're going to now have the integral of 1 minus the cos 2 2, 2, 2.
01:05
Times 5 theta over 2 d theta.
01:17
And from here we can take out our 1 half.
01:20
We'll just have the integral of 1 minus the cos of 10 theta, d theta.
01:32
And from here we're going to split this into two integrals.
01:35
So we're going to have 1 half times all of this.
01:38
We have the integral of 1d theta minus, the integral of cos 10 theta d theta.
01:52
And the last thing we need to do before we can start actually solving your integral is a u substitution.
01:56
So we're going to say u is equal to 10 theta.
01:59
Taking the derivative of both sides, you're going to have du is equal to 10 d theta...