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
xy2y = xe−x​

Evaluate I = ∫₀2 x·e−x dx.

∫₀2 x·e−x dx
I =
2.Easy
xy12

Evaluate I = ∫12 (2x2 + 3x) dx.

f(x) = 2x2 + 3x[1, 2]
I =
3.Medium
xyπ/3y = x·cos x

Evaluate I = ∫₀π/3 x·cos x dx (x in radians).

∫₀π/3 x·cos x dx
I =
4.Medium
xy4y = 2x

The region under y = 2x from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 2x0 ≤ x ≤ 4
V =
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
xyy = 0.5x2​y = x

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

y = 0.5x2y = x
A =

Answer key

  1. 1. I = 0.594
  2. 2. I = 9.167
  3. 3. I = 0.4069
  4. 4. V = 268.1
  5. 5. A = 10.67
  6. 6. A = 0.6667

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