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 = xex​

Evaluate I = ∫₀2 x·ex dx.

∫₀2 x·ex dx
I =
2.Easy
xy−21

Evaluate I = ∫−21 (−2x3 + 6x + 6) dx.

f(x) = −2x3 + 6x + 6[−2, 1]
I =
3.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 =
4.Medium
xy01

Evaluate I = ∫01 e−x dx.

f(x) = e−x[0, 1]
I =
5.Hard
xy3y = x²eˣ

Evaluate I = ∫₀3 x²·eˣ dx.

∫₀3 x²eˣ dx
I =
6.Hard
xy−11

Find the area A of the region between the parabola y = 1 − x² and the x-axis.

y = 1 − x²
A =

Answer key

  1. 1. I = 8.389
  2. 2. I = 16.5
  3. 3. V = 268.1
  4. 4. I = 0.6321
  5. 5. I = 98.43
  6. 6. A = 1.333

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