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
xy−12

Evaluate I = ∫−12 (3x2 − 3x + 7) dx.

f(x) = 3x2 − 3x + 7[−1, 2]
I =
2.Easy
xy−10

Evaluate I = ∫−10 (−4x3 − 6x + 7) dx.

f(x) = −4x3 − 6x + 7[−1, 0]
I =
3.Medium
xy1y = √(4x)

The region under y = √(4x) from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(4x)0 ≤ x ≤ 1
V =
4.Medium
xy01

Evaluate I = ∫01 e−0.5x dx.

f(x) = e−0.5x[0, 1]
I =
5.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 =
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. I = 25.5
  2. 2. I = 11
  3. 3. V = 6.283
  4. 4. I = 0.7869
  5. 5. V = 428.9
  6. 6. V = 48.48

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