problem 1:

problem 2:

please write the full solutions because i'm a integration newbie(Happy)

and a very happy christmas and new year,from India(Party)

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- December 23rd 2010, 08:41 AMearthboy2 integrals...
**problem 1**:

**problem 2**:

please write the full solutions because i'm a integration newbie(Happy)

and a very happy christmas and new year,from India(Party) - December 23rd 2010, 09:39 AMSoroban
Hello, earthboy!

The first one requires Olympic-level gymnastics.

I hope you're up for it . . .

Quote:

To the denominator, add and subtract

. .

. .

. .

The integral becomes: .

Let:

Substitute: .

Back-substitute: .

- December 23rd 2010, 10:31 AMArchie Meade
- December 23rd 2010, 06:56 PMTheCoffeeMachine
- December 23rd 2010, 07:51 PMDrexel28
- December 25th 2010, 06:41 PMearthboy
- December 26th 2010, 02:45 PMArchie Meade
Using the cos(A+B) identity..

Using

gives an incorrect answer for the area between the curve and the x-axis,

since the graph of the function crosses the x-axis twice between and

Hence, the x-axis crossing points are at

and at

Inverting the negative sign for the integral in the middle part, the area is

which gives

- December 26th 2010, 03:25 PMDrexel28
- December 26th 2010, 03:28 PMTheCoffeeMachine
- December 26th 2010, 03:33 PMDrexel28
I'd like to remark that one can do in general and what is interesting (not really 'unbelievable' though if you see why) is that .

- December 26th 2010, 03:43 PMArchie Meade
Yes, definite integral answer is fine for average value over the interval.

Alternative for area (application of integration). - December 26th 2010, 05:10 PMTheCoffeeMachine
- December 26th 2010, 06:13 PMDrexel28