Solve the following problem using trig substitution:

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- Dec 17th 2010, 08:54 AMdrewbearIntegral - trigonometric substitution?
Solve the following problem using trig substitution:

- Dec 17th 2010, 09:07 AMsnowtea
I think you forgot a dx.

Let

Now, its split into one simple integral and a trig sub .

Use - Dec 17th 2010, 09:14 AMdrewbear
i did forget the dx, sorry.

but wouldn't and not - Dec 17th 2010, 09:16 AMsnowtea
Yes, you are absolutely right :D

Let me fix that.

But you get the idea. - Dec 17th 2010, 09:17 AMTheCoffeeMachine
- Dec 17th 2010, 09:19 AMdrewbear
thank you, but is there any other way of doing this problem without setting y= to some number?

- Dec 17th 2010, 10:52 AMSoroban
Hello, drewbear!

This problem is quite awful!

Quote:

Under the radical, complete the square:

. .

The integral becomes: .

Let

Substitute: .

. . . . .

. . . . .

. . . . .

Back-substitute: .

. .

. .

We have: .

. . . . . .

This can be simplified further, but I won't bother . . . - Dec 17th 2010, 06:58 PMProve It