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−21

Evaluate I = ∫−21 (x2 + x + 1) dx.

f(x) = x2 + x + 1[−2, 1]
I =
2.Easy
xy03

Evaluate I = ∫03 (−2x3 − 5x − 4) dx.

f(x) = −2x3 − 5x − 4[0, 3]
I =
3.Medium
xy02

Evaluate I = ∫02 e−0.5x dx.

f(x) = e−0.5x[0, 2]
I =
4.Medium
xy2y = x·cos x

Evaluate I = ∫₀2 x·cos x dx (x in radians).

∫₀2 x·cos x dx
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
xy1.333y = 4xy = 3x²

The region between the line y = 4x and the parabola y = 3x² is rotated about the x-axis. Find the volume V of the solid.

y = 4xy = 3x²
V =

Answer key

  1. 1. I = 4.5
  2. 2. I = −75
  3. 3. I = 1.264
  4. 4. I = 0.4024
  5. 5. V = 428.9
  6. 6. V = 15.89

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