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
xy1y = xex​

Evaluate I = ∫₀1 x·ex dx.

∫₀1 x·ex dx
I =
2.Easy
xy14

Evaluate I = ∫14 (2x3 + 3x + 6) dx.

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

Evaluate I = ∫01 e−0.5x dx.

f(x) = e−0.5x[0, 1]
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 = 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
xy1y = 2xy = 2x²

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

y = 2xy = 2x²
V =

Answer key

  1. 1. I = 1
  2. 2. I = 168
  3. 3. I = 0.7869
  4. 4. I = 1.742
  5. 5. A = 0.6667
  6. 6. V = 1.676

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