Posted by sol on Thursday, April 5, 2012 at 10:11am.
find the volume of the solid bounded above by the surface z=f(x,y) and below by the plane region R
f(x,y)=2x^2 y;R is the region bounded by the graphs of y=x and y=x^2

calculus  Steve, Thursday, April 5, 2012 at 2:45pm
v = ∫∫R f(x,y) dA
= ∫[0,1]∫[x,x^2] 2x^2 y dy dx
= ∫[0,1] (x^2 y^2)[x,x^2] dx
= ∫[0,1] (x^6  x^4) dx
= (1/7 x^7  1/5 x^5)[0,1]
= 1/7  1/5
= 2/35

calculus  PS  Steve, Thursday, April 5, 2012 at 2:47pm
Oops. That sign is reversed, since y f goes from x^2 to x.
Answer is 2/35
Couldn't figure how I got a minus value for a function that is positive over the region.
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