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
xy1.5y = xex/2​

Evaluate I = ∫₀1.5 x·ex/2 dx.

∫₀1.5 x·ex/2 dx
I =
2.Easy
xy−11

Evaluate I = ∫−11 (−2x3 + 2) dx.

f(x) = −2x3 + 2[−1, 1]
I =
3.Medium
xy03

Evaluate I = ∫03 e−x dx.

f(x) = e−x[0, 3]
I =
4.Medium
xy15

Evaluate I = ∫15 2/x dx.

f(x) = 2/x[1, 5]
I =
5.Hard
xyy = 2x2​y = 2x

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

y = 2x2y = 2x
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 = 1.883
  2. 2. I = 4
  3. 3. I = 0.9502
  4. 4. I = 3.219
  5. 5. A = 0.3333
  6. 6. A = 1.333

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