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
xy01

Evaluate I = ∫01 (−3x2 + 3x − 5) dx.

f(x) = −3x2 + 3x − 5[0, 1]
I =
2.Easy
xy−2−1

Evaluate I = ∫−2−1 (−2x3 − 4) dx.

f(x) = −2x3 − 4[−2, −1]
I =
3.Medium
xy26

Evaluate I = ∫26 2/x dx.

f(x) = 2/x[2, 6]
I =
4.Medium
xy13y = x ln x

Evaluate I = ∫₁3 x·ln x dx.

∫₁3 x ln x dx
I =
5.Hard
xyy = x2​y = x

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

y = x2y = x
A =
6.Hard
xy−22

Find the area A of the region between the parabola y = 4 − x² and the x-axis.

y = 4 − x²
A =

Answer key

  1. 1. I = −4.5
  2. 2. I = 3.5
  3. 3. I = 2.197
  4. 4. I = 2.944
  5. 5. A = 0.1667
  6. 6. A = 10.67

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