# Are you interesting about average value if so trying here.

1. Nov 15, 2008

### memomath

Hello

here you have the same question in the enclosed

What is the average value?

average value for (exp $$\alpha$$Z ) = $$\int$$$$\int$$ exp$$\alpha$$Z ds / $$\int$$$$\int$$ ds

Over the sphere S: X^2+Y^2+Z^2=a^2

Also by use the parameterization

X= a sinϴ cos ɸ
Y= a sinϴ sin ɸ
Z= a cos ϴ

And the usual substitution t = cos ϴ in the integral:

$$0\int$$$$\Pi$$ f (cos ϴ) sinϴ dϴ =$$-1\int$$1 f(t) dt

Thanks

Last edited: Nov 25, 2008
2. Nov 16, 2008

### memomath

No comments or solution until now!!!

3. Nov 16, 2008

### HallsofIvy

Again, Word files are notorious for harboring viruses. I will not open one from someone I do not know.

4. Nov 16, 2008

### memomath

Hello here the same question in the enclosed

What is the average value?

average value for (exp $$\alpha$$Z ) = $$\int$$$$\int$$ exp$$\alpha$$Z ds / $$\int$$$$\int$$ ds

Over the sphere S: X^2+Y^2+Z^2=a^2

Also by use the parameterization

X= a sinϴ cos ɸ
Y= a sinϴ sin ɸ
Z= a cos ϴ

And the usual substitution t = cos ϴ in the integral:

$$0\int$$$$\Pi$$ f (cos ϴ) sinϴ dϴ =$$-1\int$$1 f(t) dt

Thanks

5. Nov 18, 2008

I can kind of guess what you mean, but your notation is pretty bad. I do not know what exp$$\:^\alpha Z$$ is supposed to be. Your substitution seems wrong, your notation is unorthodox and you write factors like -1 instead of just a - . This is probably the reason why people don't answer.

You might have better chances if you wrote something like:

"I am trying to get the average $$\left< f(z) \right>_{S_a}$$ of a function $$f(z)= \alpha ^ z$$ over a sphere $$S_a$$ of radius $$r=\sqrt{a}$$. I swear this is not for homework.

What I have so far is this:

$$\left< f(z) \right>_{S_a} = \frac{\int_{S_a} \alpha^z\,\mathrm{d}\Omega}{\int_{S_a} \,\mathrm{d}\Omega}$$

I tried to express the integral in polar coordinates:
X= a sinϴ cos ɸ
Y= a sinϴ sin ɸ
Z= a cos ϴ
$$\theta \in \left[0,\pi \right]$$
$$\phi \in \left[0,2\pi \right]$$

and found:
$$\int_{S_a} f(z) \,\mathrm{d}\Omega = \int_0^{\pi} f(\cos \theta) \sin \theta \, \mathrm{d}\theta$$

Is this correct? How do I proceed?"

Then people would have told you what you did wrong.

6. Nov 24, 2008

### memomath

Thanks for reply but it is not correct hint and I think you don’t proceed with the right way for the real problem you probably fix some thing else many things missing from the real posted thank you

Last edited by a moderator: Nov 26, 2008
7. Nov 24, 2008

### girlmatrix

Re: Are you interesting about average value if so trying here.ENGINEERING MATHEMATICS

YES memomath I belive there are some mistakes and the good hint to the correct answer for this problem would be in ENGINEERING MATHEMATICS JOHN BIRD