Question

could i get some help with this?

Answer 1

@TuringTest ,can u plz try this ?

Answer 2

you need the intersection of the two shapes, have you got that yet?

Answer 3

nope...

Answer 4

set formulas for z equal and find what shape the intersection is

Answer 5

a circle with a radius of 4

Answer 6

the shape of intersection

Answer 7

then..?

Answer 8

then what are the bounds on r and theta?

Answer 9

0<r<4 and 0<theta<2 pi

Answer 10

what do i integrate over though??

Answer 11

z upper - z lower

Answer 12

which function is on top and which is below for z?

Answer 13

r-(32-r^2)^(1/2)

Answer 14

yes

Answer 15

yea i never know when a function is on top or on the bottom can we plug in values to figure this out?

Answer 16

sure, try x=y=0 and you can find out real quick

Answer 17

oh, and I see I let you do it backwards, sorry

Answer 18

i got it right but i guessed...whats the math behind it?

Answer 19

hooray :)

at the origin x=y=0, so
z=x^2+y^2=0 is on the bottom, and
z=32-x^2-y^2=32 is on top

Answer 20

hmm i get it plug in x=y=0 to find out which ones on top which ones on the bottom

Answer 21

=)!

Answer 22

could you have a look at the second question as well

Answer 23

by plugging in x=y=0 and comparing values we are asking which one is on top at that point. Unless they cross each other that goes for the whole shape
the second one looks a little harder, let me see...

Answer 24

a strip of the shaded area is

Answer 25

yup with u

Answer 26

sorry that's

Answer 27

how did u get the equation of the strip

Answer 28

i got the first equation when i apply
the top-bottom rule

Answer 29

right, but I think we want to do this in polar anyways

Answer 30

yea we do
so the bottom equation is right because we want to subtract one to gt the bottom half of the circle

Answer 31

http://math.berkeley.edu/~scanez/courses/math53/spring06/problems/review2_solns.pdf

Answer 32

check this out instead=) incase your curious