- #1
Krayfish
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Homework Statement
Find the volume of the solid enclosed by the paraboloid z=x^2 + 3y^2 and the planes x=0, y=x, y=1, z=0
Homework Equations
I'm not really sure what's getting me about this, but I'm not really sure how to proceed after finding the x, y, and z intercepts...
The Attempt at a Solution
x intercept: 0
y intercept: 0
z intercept: 0
Would I just take bounds of y to be 1 and x and the bounds of x to be 0 and 1?
∫∫x^2 + 3y^2 dydx → The dy result would be yx^2 + y^3 → (x^3+x^3 -(x^2+1)) → 2X^3 - x^2 - 1 and then continue to integrate... ∫2x^3-x^2-1 dx → ((x^4)/2 -(x^2)/3 -x) → 1/2 - 1/3 - 1 = -5/6?
If that correct or am I missing something important?