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
xy1y = xe−x​

Evaluate I = ∫₀1 x·e−x dx.

∫₀1 x·e−x dx
I =
2.Easy
xy02

Evaluate I = ∫02 (−x2 + 5x − 2) dx.

f(x) = −x2 + 5x − 2[0, 2]
I =
3.Medium
xyπ/3y = x·cos x

Evaluate I = ∫₀π/3 x·cos x dx (x in radians).

∫₀π/3 x·cos x dx
I =
4.Medium
xy15y = x ln x

Evaluate I = ∫₁5 x·ln x dx.

∫₁5 x ln 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
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =

Answer key

  1. 1. I = 0.2642
  2. 2. I = 3.333
  3. 3. I = 0.4069
  4. 4. I = 14.12
  5. 5. A = 36
  6. 6. I = 12.78

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