00:01
In this question, we are asked to use u substitution to calculate the given definite integral.
00:08
And we will take u to be equal to 4 plus 3 times sine x.
00:14
Then, du will be equal to 3 times cosine x d x.
00:21
And therefore, cosine x d x will be equal to 1 3 3rd du.
00:30
We also need to change the limits of integration.
00:34
To get the new upper limit of iteration, we need to plus plus.
00:38
In the old limit for x in the expression for you to get 4 plus 3 sine pi over 2 and since sine pi over 2 equals to 1 we are going to get 7 to get the new lower limit we need to plug in the old lower limit for x in the expression for you and since to get 4 plus 3 sine 0 and since since sine 0 is 0, we are going to get 4.
01:11
Therefore, we can rewrite the whole, the integral in terms of u, as the integral from 4 to 7, cosine x d x becomes 1 third d u, and 1 over 4 plus 3 sine x cubed becomes 1 over u cube...