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
xy1y = 3x

The region under y = 3x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 3x0 ≤ x ≤ 1
V =
2.Easy
xy−10

Evaluate I = ∫−10 (−2x2 − 3x + 6) dx.

f(x) = −2x2 − 3x + 6[−1, 0]
I =
3.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)1 dx.

f(x) = 2x·(x² + 1)1[0, 2]
I =
4.Medium
xyπ/3y = x·cos x

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

∫₀π/3 x·cos x dx
I =
5.Hard
xy1y = x²eˣ

Evaluate I = ∫₀1 x²·eˣ dx.

∫₀1 x²eˣ dx
I =
6.Hard
xyy = 2x2​y = 3x

Find the area A of the region enclosed by y = 2x2 and y = 3x.

y = 2x2y = 3x
A =

Answer key

  1. 1. V = 9.425
  2. 2. I = 6.833
  3. 3. I = 12
  4. 4. I = 0.4069
  5. 5. I = 0.7183
  6. 6. A = 1.125

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