Recent content by 3soteric

the jacobian equals 3 but how is that related to the entire problem ? :s

Homework Statement use the substitution u= x+y and v=y-2x to evaluate double integral from ∫1-0∫(1−x) -(0) of (√x+y) (y−2x)^2 dydx Homework Equations integration tables I am assuming The Attempt at a Solution i tried to integrate directly but none of my integration tables match...

correction answer is pi/6 right?

yep basically i did this ∫2pi-0 ∫1-0 ∫ 1-(-1) z^2 r^3 dz dr dtheta i multiplied z^2r^2 by r so i got r^3 (first digit means upper limit for integral)

my answer ended up being 4pi/9!

will do ! ill post back with results thank you

i conclude z^2 (r^2 cos^2 theta + r^2 sin^2 theta) so i can factor the r^2 as well and I am left with (sin ^2 + cos ^2) and that's one so z^2 r^2?

can i use sin^2+cos^2=1 then basically do z^2 r^2 + z^2 r^2 which is 2z^2r^2?

by the way thanks for helping dick

the function i will integrate will be z^2 x^2 + x^2 y^2 which i need to convert so its z^2 (r^2 cos^2theta) + z^2 (r^2 sin^2 theta) i integrate that? if so do i integrate rdzdrdtheta or rdrdzdtheta? i can't find a limit for dz, is it just -1 to 1? i don't have to express in other...

i got the following limits, r ≤ 1, 0≤ theta ≤ 2pi , -1≤z≤1 thats in polar right? now do i integrate? rdrdzdtheta?

if i draw the xz and yz traces, will it be a horizontal line at 1 and at -1? then of course the xy trace is a circle with r=1

can i integrate the first limit then convert to polar? or do i have to flat out use cylindrical coordinates?

thank you dick! I am on it right now ! ill post results