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 = xe2x​

Evaluate I = ∫₀2 x·e2x dx.

∫₀2 x·e2x dx
I =
2.Easy
xy−12

Evaluate I = ∫−12 (−4x3 + 2x − 3) dx.

f(x) = −4x3 + 2x − 3[−1, 2]
I =
3.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 2]
I =
4.Medium
xy2y = 0.5x

The region under y = 0.5x from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 2
V =
5.Hard
xyy = 2x2​y = x

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

y = 2x2y = x
A =
6.Hard
xyy = x2​y = 3x

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

y = x2y = 3x
A =

Answer key

  1. 1. I = 41.2
  2. 2. I = −21
  3. 3. I = 41.33
  4. 4. V = 2.094
  5. 5. A = 0.04167
  6. 6. A = 4.5

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