Find the area under the curve

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- Jul 1st 2007, 11:52 AMcamherokidIntergration by substitution 2
Find the area under the curve

- Jul 1st 2007, 12:03 PMJhevon

The area under the curve between the limits is given by:

We proceed by substitution

Let

Also, when

and when ..........we can use these to change the limits (I wouldn't, but that seems to be the preferred method around here, i always back-substitute to get the integral as a function of x and plug in the old limits)

And i think you can take it from there - Jul 1st 2007, 12:05 PMred_dog
Let .

Substitution: .

Then .

So