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−12

Evaluate I = ∫−12 (−2x2 + 2x + 4) dx.

f(x) = −2x2 + 2x + 4[−1, 2]
I =
2.Easy
xy2y = xe−x​

Evaluate I = ∫₀2 x·e−x dx.

∫₀2 x·e−x dx
I =
3.Medium
xy13

Evaluate I = ∫13 2/x dx.

f(x) = 2/x[1, 3]
I =
4.Medium
xy03

Evaluate I = ∫03 e0.5x dx.

f(x) = e0.5x[0, 3]
I =
5.Hard
xy1.333y = 4xy = 3x²

The region between the line y = 4x and the parabola y = 3x² is rotated about the x-axis. Find the volume V of the solid.

y = 4xy = 3x²
V =
6.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 =

Answer key

  1. 1. I = 9
  2. 2. I = 0.594
  3. 3. I = 2.197
  4. 4. I = 6.963
  5. 5. V = 15.89
  6. 6. A = 0.6667

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