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
xy03

Evaluate I = ∫03 (4x2 + 5x + 2) dx.

f(x) = 4x2 + 5x + 2[0, 3]
I =
2.Easy
xy−11

Evaluate I = ∫−11 (x3 − 1) dx.

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

Evaluate I = ∫01 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 1]
I =
4.Medium
xy1y = x·cos x

Evaluate I = ∫₀1 x·cos x dx (x in radians).

∫₀1 x·cos x dx
I =
5.Hard
xy−33

Find the area A of the region between the parabola y = 9 − x² and the x-axis.

y = 9 − x²
A =
6.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =

Answer key

  1. 1. I = 64.5
  2. 2. I = −2
  3. 3. I = 2.333
  4. 4. I = 0.3818
  5. 5. A = 36
  6. 6. I = 3.602

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