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
xy−12

Evaluate I = ∫−12 (−3x2 − 2x − 2) dx.

f(x) = −3x2 − 2x − 2[−1, 2]
I =
2.Easy
xy13

Evaluate I = ∫13 (3x3 + 4x + 8) dx.

f(x) = 3x3 + 4x + 8[1, 3]
I =
3.Medium
xy1y = x·sin x

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

∫₀1 x·sin x dx
I =
4.Medium
xy12y = x ln x

Evaluate I = ∫₁2 x·ln x dx.

∫₁2 x ln x dx
I =
5.Hard
xy−11

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

y = 1 − x²
A =
6.Hard
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =

Answer key

  1. 1. I = −18
  2. 2. I = 92
  3. 3. I = 0.3012
  4. 4. I = 0.6363
  5. 5. A = 1.333
  6. 6. I = 12.78

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