Integrals worksheet with answers

Free printable Integrals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xy3y = 0.5x

The region under y = 0.5x from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 3
V =
2.Easy
xy2y = 2x

The region under y = 2x from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 2x0 ≤ x ≤ 2
V =
3.Medium
xy15y = x ln x

Evaluate I = ∫₁5 x·ln x dx.

∫₁5 x ln x dx
I =
4.Medium
xy02

Evaluate I = ∫02 e0.5x dx.

f(x) = e0.5x[0, 2]
I =
5.Hard
xy−33

Find the area A of the region between the parabola y = 9 − x² and the x-axis.

y = 9 − x²
A =
6.Hard
xy4y = 4xy = x²

The region between the line y = 4x and the parabola y = x² is rotated about the x-axis. Find the volume V of the solid.

y = 4xy = x²
V =

Answer key

  1. 1. V = 7.069
  2. 2. V = 33.51
  3. 3. I = 14.12
  4. 4. I = 3.437
  5. 5. A = 36
  6. 6. V = 428.9

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