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
xy02

Evaluate I = ∫02 (−3x2 + 4x + 8) dx.

f(x) = −3x2 + 4x + 8[0, 2]
I =
2.Easy
xy1.5y = xex/2​

Evaluate I = ∫₀1.5 x·ex/2 dx.

∫₀1.5 x·ex/2 dx
I =
3.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 2]
I =
4.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 1]
I =
5.Hard
xy3y = x²eˣ

Evaluate I = ∫₀3 x²·eˣ dx.

∫₀3 x²eˣ dx
I =
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 = 16
  2. 2. I = 1.883
  3. 3. I = 41.33
  4. 4. I = 3.75
  5. 5. I = 98.43
  6. 6. V = 15.89

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