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
xy14

Evaluate I = ∫14 (−x2 − 2x + 5) dx.

f(x) = −x2 − 2x + 5[1, 4]
I =
2.Easy
xy−11

Evaluate I = ∫−11 (2x2 − 4x − 1) dx.

f(x) = 2x2 − 4x − 1[−1, 1]
I =
3.Medium
xy12.5y = x ln x

Evaluate I = ∫₁2.5 x·ln x dx.

∫₁2.5 x ln x dx
I =
4.Medium
xy2y = x·sin x

Evaluate I = ∫₀2 x·sin x dx (x in radians).

∫₀2 x·sin x dx
I =
5.Hard
xyy = x2​y = 2x

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

y = x2y = 2x
A =
6.Hard
xy−33

Find the area A of the region between the parabola y = 9 − x² and the x-axis.

y = 9 − x²
A =

Answer key

  1. 1. I = −21
  2. 2. I = −0.6667
  3. 3. I = 1.551
  4. 4. I = 1.742
  5. 5. A = 1.333
  6. 6. A = 36

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