1. Jul 26, 2010

### optics.tech

Hello everyone,

This one makes me very confuse!

Can someone please tell me how to solve the following integration?

1. The problem statement, all variables and given/known data
Solve the following integration:

2. Relevant equations
integral (x cos^2(x) / (1 + x)^1/2) dx

3. The attempt at a solution
Confuse

If above equation isn't clear enough, please see below image:

[PLAIN]http://img148.imageshack.us/img148/6692/70786744.png [Broken]

Thank you very much for your help.

Last edited by a moderator: May 4, 2017
2. Jul 26, 2010

### sagardip

Are you sure that this integral is solvable????I think it requires the use of incomplete Gamma Function.But then this integral is not solvable for real x

3. Jul 26, 2010

### optics.tech

I've tried to solve it by integration techniques in the very basic english calculus textbook but I couldn't find a method to solve it.

This exercise is from Exploring Numerical Methods - An Introduction to Scientific Computing Using MATLAB book by Peter Linz and Richard L. C. Wang.

I couldn't find any hints on above book too.

Maybe I should read further chapters.

4. Jul 26, 2010

### Staff: Mentor

A problem like this in a book on numerical methods is most likely intended to be solved by numerical methods, such as the Simpson's Method.

5. Jul 26, 2010

### optics.tech

Hello Mark44,

Why can you with certainty point to The Simpson's method?

Please I want to know it too especially algebraically.

Thank you

Huygen

6. Jul 26, 2010

### Char. Limit

The integral, surprisingly enough, doesn't require use of the incomplete gamma, but it does need the imaginary error function erfi(x) defined as...

$$erfi(x) = \frac{\sqrt{\pi} \int e^{-\left(i x\right)^2}}{2 i}$$

At least I believe that's how it's defined. It's also functionally equal to...

$$erfi(x) = \frac{erf\left(i x\right)}{i}$$

Proof by computer is found here.

7. Jul 27, 2010

### hgfalling

Simpson's rule is a method of approximating an integral by evaluating the function at various points:

http://en.wikipedia.org/wiki/Simpson's_rule

Learning about things like this is what a Numerical Methods class is basically about.

8. Jul 28, 2010

### snshusat161

Maybe its typo and it is cos 2 x inspite of cos ^2 x

9. Jul 28, 2010

### Staff: Mentor

I doubt it very much, as it is written as cos2(x) in the integral.

10. Jul 28, 2010

### snshusat161

but such question is very difficult to solve in precalculus mathematics. I don't know the solution or any way to solve it cause I had left solving maths from last 3 months. (holiday's going) but after going through other members answer I'm forced to think there is some typo.

@OP, btw, in which class you are?

11. Jul 28, 2010

### Staff: Mentor

Not only that, it's pretty much impossible. Courses before calculus don't work with differentiation or integration.
The OP said the exercise is from a book on numerical methods.

12. Jul 29, 2010

### HallsofIvy

Why "certainty"? Mark44 said "most likely intended to be solved by numerical methods, such as the Simpson's Method" (emphasis mine).

That's hardly implying "certainty" that you should use Simpson's method! But if this is in a text on numerical methods and is asking you to integrate a function, I'd be very surprised if Simpson's method was not explained just a few pages earlier.

13. Aug 2, 2010

### optics.tech

No, I'm sure I was typed the correct equation.

Yes, I'm sure that there is no The Simpson's method is explained before.

Yes, as I was already told before, I wasn't able to solve the equation with any basic integration techniques on basic calculus textbook.

14. Aug 2, 2010

### optics.tech

I wonder if I may typed the complete exercise of this in this forums?

15. Aug 2, 2010

### HallsofIvy

Then I will go ahead and move this thread to the "Calculus" homework section. An integral itself is hardly "pre-calculus".

16. Aug 3, 2010

### optics.tech

If I'm not mistake on understanding, I deem it as yes.

17. Aug 3, 2010

### optics.tech

Here are the exercises from the book:

Last edited by a moderator: May 4, 2017
18. Aug 3, 2010