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 (2x2 + 5x + 8) dx.

f(x) = 2x2 + 5x + 8[1, 2]
I =
2.Easy
xy01

Evaluate I = ∫01 (4x2 − 2x + 1) dx.

f(x) = 4x2 − 2x + 1[0, 1]
I =
3.Medium
xy12

Evaluate I = ∫12 4/x dx.

f(x) = 4/x[1, 2]
I =
4.Medium
xy2y = x·sin x

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

∫₀2 x·sin x dx
I =
5.Hard
xy−22

Find the area A of the region between the parabola y = 4 − x² and the x-axis.

y = 4 − x²
A =
6.Hard
xy2y = xy = 0.5x²

The region between the line y = x and the parabola y = 0.5x² is rotated about the x-axis. Find the volume V of the solid.

y = xy = 0.5x²
V =

Answer key

  1. 1. I = 20.17
  2. 2. I = 1.333
  3. 3. I = 2.773
  4. 4. I = 1.742
  5. 5. A = 10.67
  6. 6. V = 3.351

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