integrate

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- July 17th 2010, 10:37 PMPunchintegrate
integrate

- July 17th 2010, 10:48 PMProve It
.

Let so that and .

The integral becomes:

. - July 18th 2010, 09:16 AMSoroban
Hello, Punch!

Another method . . .

Quote:

Integrate: .

We have: .

Let: .

Substitute: .

. . . . . . .

Back-substitute: .

. . . . . . . . . .

. . . . . . . . . .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Some advice (welcome or not):

When given aexpression under a radical,*linear*

. . let

Given: .an integral with

. . and the new integral will have no radicals (usually).

- July 18th 2010, 09:32 AMAlso sprach Zarathustra
And another solution...

By substitution: x=(1/2)cos(2t). dx=-sin(2t), sqrt(2x+1)=sqrt(cos(2t)+1)=sqrt(2cos^2(t))=sqrt(2) *cos(t)

Ok... maybe it's a little bit complicated...