Find the exact value of

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- Aug 15th 2011, 12:31 AMPunchdefinite intergral
Find the exact value of

- Aug 15th 2011, 12:34 AMPunchRe: definite intergral

- Aug 15th 2011, 01:14 AMProve ItRe: definite intergral

Now make the substitution . Also note that when and when . The integral becomes

- Aug 15th 2011, 01:30 AMPunchRe: definite intergral
Thank you for your help but there is something i need to clarify. I remember my teacher telling me that all substitution questions comes with a given substitute. This question, however, does not come with one. How then did you realise that this question requires a substitution? And would it be appropriate to do substitution for a question that doesn't come with a given substitute?

- Aug 15th 2011, 01:49 AMProve ItRe: definite intergral
The point of substitution is to be able to find an "inner function" multiplied by the inner function's derivative. With trigonometric functions, I tend to convert them to sines and cosines if possible, because they are each others derivatives (up to a constant multiple) and it is easy to use identities to get the function to a function of sine or a function of cosine only (except for the multiple of the other to be used as the derivative). In this case, I had to convert it to a function of sine (the "inner function"), multiplied by a single cosine (the derivative of the inner function).