Multivariable Calculus - midterm questions

[s8on95]

I have two problems I need help with

1. Homework Statement

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 givenIn 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.

 

[theodoros.mihos]

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

 

[s8on95]

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

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.

 

[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.

 

[SammyS]

I have two problems I need help with

1. Homework Statement

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

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.

 

[s8on95]

Thank you both, it makes sense.