Question

Find the volume of the solid d bounded by the paraboloid s : z = 25 x 2 y 2 and the xy-plane

Answer 1

Hi...

To compute the volume of the given region, we will be using the triple integrals formula in cylindrical coordinates, which is:

V=∫βα∫h2(θ)h1(θ)∫u2(rcosθ,rsinθ,z)u1(rcosθ,rsinθ,z)rf(rcosθ,rsinθ,z)dzdrdθV=∫αβ∫h1(θ)h2(θ)∫u1(rcos⁡θ,rsin⁡θ,z)u2(rcos⁡θ,rsin⁡θ,z)rf(rcos⁡θ,rsin⁡θ,z)dzdrdθ

We will also use the following conversion formulas:

r2=x2+y2,x=rcosθ,y=rsinrθ.

hope it'll help you...

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