Wednesday 11 March 2015

`int cos^4(theta) sin(theta) d theta` Evaluate the indefinite integral.

You need to use the following substitution  `cos theta = u` , such that:


`cos theta = u=> -sin theta d theta = du =>sin theta d theta = -du`


`int cos^4 theta*sin theta d theta = - int u^4 du`


`- int u^4 du = -(u^5)/5 + c`


Replacing back   `cos theta` for` u` yields:


`int cos^4 theta*sin theta d theta = -((cos theta)^5)/5 + c`


Hence, evaluating the indefinite integral, yields `int cos^4...

You need to use the following substitution  `cos theta = u` , such that:


`cos theta = u=> -sin theta d theta = du =>sin theta d theta = -du`


`int cos^4 theta*sin theta d theta = - int u^4 du`


`- int u^4 du = -(u^5)/5 + c`


Replacing back   `cos theta` for` u` yields:


`int cos^4 theta*sin theta d theta = -((cos theta)^5)/5 + c`


Hence, evaluating the indefinite integral, yields `int cos^4 theta*sin theta d theta = -((cos theta)^5)/5 + c`

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