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
xy1y = 0.5x

The region under y = 0.5x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 1
V =
2.Easy
xy−12

Evaluate I = ∫−12 (−3x3 − 5x + 2) dx.

f(x) = −3x3 − 5x + 2[−1, 2]
I =
3.Medium
xy1y = 2x

The region under y = 2x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 2x0 ≤ x ≤ 1
V =
4.Medium
xy2y = x

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

y = x0 ≤ x ≤ 2
V =
5.Hard
xy0.5y = x²eˣ

Evaluate I = ∫₀0.5 x²·eˣ dx.

∫₀0.5 x²eˣ dx
I =
6.Hard
xy1.667y = 5xy = 3x²

The region between the line y = 5x and the parabola y = 3x² is rotated about the x-axis. Find the volume V of the solid.

y = 5xy = 3x²
V =

Answer key

  1. 1. V = 0.2618
  2. 2. I = −12.75
  3. 3. V = 4.189
  4. 4. V = 8.378
  5. 5. I = 0.0609
  6. 6. V = 48.48

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