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 + 5x + 2) dx.

f(x) = 2x2 + 5x + 2[1, 2]
I =
2.Easy
xy1.5y = xex/2​

Evaluate I = ∫₀1.5 x·ex/2 dx.

∫₀1.5 x·ex/2 dx
I =
3.Medium
xy16y = x ln x

Evaluate I = ∫₁6 x·ln x dx.

∫₁6 x ln x dx
I =
4.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 2]
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
xyy = 0.5x2​y = 4x

Find the area A of the region enclosed by y = 0.5x2 and y = 4x.

y = 0.5x2y = 4x
A =

Answer key

  1. 1. I = 14.17
  2. 2. I = 1.883
  3. 3. I = 23.5
  4. 4. I = 41.33
  5. 5. A = 1.333
  6. 6. A = 42.67

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