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@TuringTest ,can u plz try this ?
you need the intersection of the two shapes, have you got that yet?
set formulas for z equal and find what shape the intersection is
a circle with a radius of 4
the shape of intersection
then what are the bounds on r and theta?
what do i integrate over though??
z upper - z lower
which function is on top and which is below for z?
yea i never know when a function is on top or on the bottom can we plug in values to figure this out?
sure, try x=y=0 and you can find out real quick
oh, and I see I let you do it backwards, sorry
i got it right but i guessed...whats the math behind it?
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
hmm i get it plug in x=y=0 to find out which ones on top which ones on the bottom
could you have a look at the second question as well
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...
a strip of the shaded area is|dw:1352743660838:dw|
yup with u
how did u get the equation of the strip
i got the first equation when i apply the top-bottom rule
right, but I think we want to do this in polar anyways
yea we do so the bottom equation is right because we want to subtract one to gt the bottom half of the circle
check this out instead=) incase your curious