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−11

Evaluate I = ∫−11 (3x3 − 2x − 2) dx.

f(x) = 3x3 − 2x − 2[−1, 1]
I =
2.Easy
xy−12

Evaluate I = ∫−12 (x2 + 5x − 2) dx.

f(x) = x2 + 5x − 2[−1, 2]
I =
3.Medium
xy03

Evaluate I = ∫03 e2x dx.

f(x) = e2x[0, 3]
I =
4.Medium
xy12

Evaluate I = ∫12 5/x dx.

f(x) = 5/x[1, 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 = 2x2​y = 4x

Find the area A of the region enclosed by y = 2x2 and y = 4x.

y = 2x2y = 4x
A =

Answer key

  1. 1. I = −4
  2. 2. I = 4.5
  3. 3. I = 201.2
  4. 4. I = 3.466
  5. 5. A = 1.333
  6. 6. A = 2.667

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