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
xy12

Evaluate I = ∫12 (2x3 − 4x + 2) dx.

f(x) = 2x3 − 4x + 2[1, 2]
I =
2.Easy
xy3y = √(x)

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

y = √(x)0 ≤ x ≤ 3
V =
3.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 1]
I =
4.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 2]
I =
5.Hard
xyy = 0.5x2​y = 3x

Find the area A of the region enclosed by y = 0.5x2 and y = 3x.

y = 0.5x2y = 3x
A =
6.Hard
xy−33

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

y = 9 − x²
A =

Answer key

  1. 1. I = 3.5
  2. 2. V = 14.14
  3. 3. I = 3.75
  4. 4. I = 41.33
  5. 5. A = 18
  6. 6. A = 36

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