# Multivariable Calculus - midterm questions

1. Jun 9, 2015

### s8on95

I have two problems I need help with

1. The problem statement, all variables and given/known data

https://ccle.ucla.edu/mod/resource/view.php?id=801511
https://ccle.ucla.edu/mod/resource/view.php?id=778704

2,3. Answers and work are given

In the surface integral problem, I do not understand how it sets it up for Method 1. (How does it go from integral of x2+y2 to 2/3 integral of x2+y2+z2

For the "estimate the integral" problem, I do not understand why e(sinx cosx sinz) is considered a constant function.

Also, any cramming advice for passing a computation multivariable calc test would be appreciated.

2. Jun 9, 2015

### theodoros.mihos

Total integers, with symmetry limits have 2/3 ratio.

3. Jun 9, 2015

### s8on95

Could you explain that with more detail. The phrases total integers and symmetry limits do not appear in my textbook and google isn't much help.

4. Jun 9, 2015

### theodoros.mihos

Make integrations with independent variables.
$$\int_{-a}^{a}\int_{-a}^{a}\int_{-a}^{a}dxdydz \,\text{and}\, \int_{-a}^{a}\int_{-a}^{a}dxdy$$
They are for cube but the ratio is the same for symmetric integration limits. To make the 2nd integral directlly have much more work.

5. Jun 9, 2015

### SammyS

Staff Emeritus
By symmetry, each of the following integrals gives the same value.

$\displaystyle \ \iint_{S} x^2\, dA=\iint_{S} y^2\, dA=\iint_{S} z^2\, dA\$

You will usually get better response if you can post the images of your work directly.

Better yet, is to use LaTeX OR all the nice little symbols PF has provided for you.

6. Jun 10, 2015

### s8on95

Thank you both, it makes sense.