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 − 3x + 2) dx.

f(x) = 2x2 − 3x + 2[1, 2]
I =
2.Easy
xy−20

Evaluate I = ∫−20 (−x2 − 5x − 5) dx.

f(x) = −x2 − 5x − 5[−2, 0]
I =
3.Medium
xy3y = 3x

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

y = 3x0 ≤ x ≤ 3
V =
4.Medium
xy03

Evaluate I = ∫03 ex dx.

f(x) = ex[0, 3]
I =
5.Hard
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =
6.Hard
xyy = x2​y = 2x

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

y = x2y = 2x
A =

Answer key

  1. 1. I = 2.167
  2. 2. I = −2.667
  3. 3. V = 254.5
  4. 4. I = 19.09
  5. 5. I = 12.78
  6. 6. A = 1.333

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