Tag-Archive for » games «

Calculus Volume Problems

Please help me with one of my Calculus Volume Problems!

y =3x
y=x^2
rotated around x=3

I thought 486/4 pi was the right answer, but it isn’t. Help please.

Use the cylindrical method.

V = 2π ∫[a,b] p(x)h(x) dx

The 2 functions are equal at 0 and 3, these are the limits.
p(x) = 3 – x
h(x) = 3x – x²

V = 2π ∫[0,3] (3 – x)(3x – x²) dx
V = 2π ∫[0,3] (9x – 6x² + x³) dx
V = 2π * ((x⁴/4) – 2x³ + (9x²/2))|[0,3]
V = 2π * ((81/4) – 2(27) + (81/2) – 0)
V = 2π((81/4) – (216//4) + (162/4))
V = 2π(27/4) = 27π/2 ≈ 42.4115

Checked with Maple.

Multiple Integrals 9: Finding Volume Problems (Cylinder)