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
xy13

Evaluate I = ∫13 (3x2 + 3x − 4) dx.

f(x) = 3x2 + 3x − 4[1, 3]
I =
2.Easy
xy12

Evaluate I = ∫12 (4x3 + 6x + 1) dx.

f(x) = 4x3 + 6x + 1[1, 2]
I =
3.Medium
xy01

Evaluate I = ∫01 e2x dx.

f(x) = e2x[0, 1]
I =
4.Medium
xy1y = x·cos x

Evaluate I = ∫₀1 x·cos x dx (x in radians).

∫₀1 x·cos x dx
I =
5.Hard
xyy = 0.5x2​y = x

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

y = 0.5x2y = x
A =
6.Hard
xy−11

Find the area A of the region between the parabola y = 1 − x² and the x-axis.

y = 1 − x²
A =

Answer key

  1. 1. I = 30
  2. 2. I = 25
  3. 3. I = 3.195
  4. 4. I = 0.3818
  5. 5. A = 0.6667
  6. 6. A = 1.333

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