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IB MATHEMATICS · CALCULUS · INTEGRATION
Volumes of Revolution in 3D · V = π∫[f(x)]² dx
Spin a flat region 360° around the x-axis and watch a solid appear. Slice it into disks, add them up, and see the sum close in on the exact value of the integral.
Drag to rotate · scroll the sliders to reshape
V ≈ 25.13
Choose the solid
b upper limit4
n number of disk slices8
x position of the cross-section2
Tip: switch to Disk slices and increase n to watch the stack of disks become the smooth solid.
The integral
Exact volumeSum of 8 disksErrorCross-section at x
Accuracy
Cross-section view
Every vertical slice of the region sweeps out a circle of area A(x) = π[f(x)]². Integrating A(x) from a to b gives the volume.
Practice
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