# Integrate This

1. Dec 29, 2005

### samalkhaiat

Happy new year for you all,
This is very nice place, So girls and boys, let me give you something to play with:
Integrate (r^.a)(r^.b)(r^.c)(r^.d) d(cos8)
from cos8=1 to cos8=-1.
a,b,c and d are constant vectors, r^ is the unit vector
(iX+jY+kZ)/|r|, 8 is the spherical angle between r^ and Z-axis.
The dot represents the scalar product.
When you have done that, do this one:

(a.r^)/(1+K.r^) d(cos8)
the limits of integration same as befor, a and K are constant vectors.

cheers

sam

2. Dec 29, 2005

### abdo375

plzzzzzzzzzzzzzzzzzzzzz take sometime and learn latex

3. Dec 29, 2005

### Tom Mattson

Staff Emeritus
:rofl: :rofl:

I have to agree, I can't really tell what's supposed to be going on there with the carets. And integrating with respect to the number 8? Is that really what you meant?

4. Dec 30, 2005

### Lisa!

I've not noticed we could use $$8$$ instead of $$\theta$$ !

Last edited: Dec 30, 2005
5. Dec 30, 2005

### Tide

$$\frac {2}{5} a b c d$$

I was tempted to say 0 because 8 is usually a constant so that d cos(8) = 0. ;)

6. Dec 30, 2005

### samalkhaiat

[
[/QUOTE]

1) I don't have that "sometime".
2) It is to complicated for my little brain.

sam

7. Dec 30, 2005

### fargoth

1) I don't have that "sometime".
2) It is to complicated for my little brain.
sam[/QUOTE]

just click on the equations and see how they wrote it... im sure youd figure it out...

8. Dec 30, 2005

### Pengwuino

Find time :)

And if you can integrate, i don't think its too complicated for you... especially with a program such as texaide

9. Dec 30, 2005

### samalkhaiat

[
The carets used to distinguish between a vector and its "unit vector":rofl::rofl:
[/QUOTE]
No. The 8 , as I said, is the spherical angle(do you remember theta), it is just a symbol:tongue2: :tongue2:

sam

10. Dec 30, 2005

### samalkhaiat

Yes darling, you could if you think of 8 as symbol.:zzz:

sam

11. Dec 30, 2005

### samalkhaiat

Yes, now this answer is write, if 8 was a number, but it is not. So,even your temptation is wrong.:tongue2: :rofl:

good luck

sam

12. Dec 30, 2005

### Tide

samal,

Prove it! :)

13. Dec 30, 2005

### samalkhaiat

14. Dec 30, 2005

### fargoth

the final answer has mixed parts of a b c and d in it, not only $$a_xb_x$$ etc. so it cant be abcd

15. Dec 30, 2005

### fargoth

16. Dec 30, 2005

### samalkhaiat

Last edited: Dec 30, 2005
17. Dec 30, 2005

### samalkhaiat

18. Dec 30, 2005

### samalkhaiat

19. Dec 31, 2005

### Lisa!

I meant I hadn't noticed te similarity, dear!

20. Dec 31, 2005

### fargoth

21. Jan 1, 2006

### samalkhaiat

22. Jan 1, 2006

### samalkhaiat

23. Jan 3, 2006

### samalkhaiat

24. Jan 4, 2006

### benorin

Here's a similar integral

If $\vec{a},\vec{b},\mbox{ and }\vec{c}$ are constant vectors, $\vec{r}$ is the position vector $\vec{r}=\left< x,y,z\right> ,$ and E is given by the inequalities

$$0\leq\vec{a}\cdot\vec{r}\leq\alpha,0\leq\vec{b}\cdot\vec{r}\leq\beta,0\leq\vec{c}\cdot\vec{r}\leq\gamma,$$

show that

$$\int\int\int \left( \vec{a}\cdot\vec{r}\right) \left( \vec{b}\cdot\vec{r}\right) \left( \vec{c}\cdot\vec{r}\right) dV =\frac{ \left( \alpha\beta\gamma\right) ^2}{8\left| \vec{a}\cdot\left( \vec{b}\times\vec{c}\right) \right|}$$

(this one comes out of Stewart, Calculus 4th ed., ch. 15 Problems Plus #4 on pg. 1038).

Enjoy .

25. Jan 4, 2006

### Integral

Staff Emeritus
So because you are to lazy to learn LaTex the rest of use must expend extra energy to translate what you write. This shows no respect for others, please show some respect, learn to use the tools provided to make this forum a better place for all.

Personally I am reluctant to bother responding to a post such as yours, other then to as learn LaTex.

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