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 (−3x3 − 4x + 2) dx.

f(x) = −3x3 − 4x + 2[1, 4]
I =
2.Easy
xy1.5y = xe−x​

Evaluate I = ∫₀1.5 x·e−x dx.

∫₀1.5 x·e−x dx
I =
3.Medium
xy01

Evaluate I = ∫01 ex dx.

f(x) = ex[0, 1]
I =
4.Medium
xy13

Evaluate I = ∫13 2/x dx.

f(x) = 2/x[1, 3]
I =
5.Hard
xy2.5y = 5xy = 2x²

The region between the line y = 5x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 5xy = 2x²
V =
6.Hard
xyy = 0.5x2​y = 3x

Find the area A of the region enclosed by y = 0.5x2 and y = 3x.

y = 0.5x2y = 3x
A =

Answer key

  1. 1. I = −215.3
  2. 2. I = 0.4422
  3. 3. I = 1.718
  4. 4. I = 2.197
  5. 5. V = 163.6
  6. 6. A = 18

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