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For doing this problem, we're going to use U sub, so we're
going to have U equaling 4 minus cosine 3T.
Once we do this U sub, we need to find our du and our DU is
going to equal derivative of a constant of four is just 0
derivative of cosine is negative sine.
So the negative and the negative are going to cancel, and then
the derivative of the three T is 3.
So we're going to get 3 sine 3T DT.
Then we need to also change our bounds.
So if T was originally π thirds, we want U of π thirds.
So we're going to say 4 minus cosine of π because π thirds
times three is π cosine of π is -1.
So 4 - -1 is going to give us a new bound of five.
And then we're also going to have U of 0.
So U is 0 is going to be 4 minus cosine of 0.
Cosine of 0 is 1/4, minus one is 3.
So our new integral is going to look like lower bound of three,
upper bound of five.
That three sine 3 TDT all is going to get replaced with our
DU.
And that 4 minus cosine 3T is our U.
So now we're going to have lane of the absolute value of U from
3:00 to 5:00.
So we're going to have lane of five minus lane of three.
Or we could write that as lane of five thirds.