- #1
coolusername
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Homework Statement
It asks to find the volume of the solid given these planes:
z = x
y = x
x + y = 2
z = 0
It also asks to find the volume using 2 iterated integrals with different orders of x and y integration.
Homework Equations
The Attempt at a Solution
I found the volume of the solid which is 1/3 by setting up the volume as
∫(x=1 --> x=0) ∫(y=2-x -->y=0) [x]dydx
which then gave me 1/3.
However, when I tried to do it by integrating with respect to x first, I get a different answer with variables of y.
∫(y=2-x -->y=0)∫(x=1 --> x=0) [x]dxdy
first integration wrt 'x': (x^2)/2 from (x=1 --> x=0) = 1/2
This would leave ∫(y=2-x -->y=0) [1/2]dy = y/2 (y=2-x -->y=0) => This gives simply variables.
What am I doing wrong?