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 = x

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

y = x0 ≤ x ≤ 1
V =
2.Easy
xy14

Evaluate I = ∫14 (3x2 − x − 1) dx.

f(x) = 3x2 − x − 1[1, 4]
I =
3.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 1]
I =
4.Medium
xy14

Evaluate I = ∫14 1/x dx.

f(x) = 1/x[1, 4]
I =
5.Hard
xyy = 2x2​y = x

Find the area A of the region enclosed by y = 2x2 and y = x.

y = 2x2y = x
A =
6.Hard
xy2y = 2xy = x²

The region between the line y = 2x and the parabola y = x² is rotated about the x-axis. Find the volume V of the solid.

y = 2xy = x²
V =

Answer key

  1. 1. V = 1.047
  2. 2. I = 52.5
  3. 3. I = 2.333
  4. 4. I = 1.386
  5. 5. A = 0.04167
  6. 6. V = 13.4

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