silemus.
← All examples
  1. 4L'Hopital's rule, limit
  2. 6Limit of (1−cos⁡x)/x2(1 - \cos x)/x^2
  3. 16Implicit differentiation, folium
  4. 21Maximizing rectangle area
  5. 22Optimizing box volume
  6. 23Related rates, sphere volume
  7. 24Related rates, circle area
  8. 27Integral of ln⁡x\ln x by parts
  9. 28Integration by parts
  10. 30Integral of sin⁡2x\sin^2 x
  11. 35Area between x2x^2 and xx
  12. 37Volume by disk method
  13. 41Telescoping series sum
  14. 44Maclaurin series of cos⁡x\cos x
  15. 45Radius of convergence, ratio test
  16. 49Double integral, inner yy first
  17. 50Separable ODE dy/dx=2ydy/dx = 2y

37Volume by disk method

The region under y=x\displaystyle y = \sqrt{x} for 0≤x≤4\displaystyle 0 \le x \le 4 is rotated about the x\displaystyle x-axis. Find the volume. Give the answer to 3 decimal places.

Rotating the region makes stacked disks of radius √x, so volume is π∫₀⁴ x dx = π·[x²/2]₀⁴ = 8π ≈ 25.133 cubic units.

How good is this answer?