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
xy2y = xe−x​

Evaluate I = ∫₀2 x·e−x dx.

∫₀2 x·e−x dx
I =
2.Easy
xy12

Evaluate I = ∫12 (−x2 − 6x + 3) dx.

f(x) = −x2 − 6x + 3[1, 2]
I =
3.Medium
xy02

Evaluate I = ∫02 ex dx.

f(x) = ex[0, 2]
I =
4.Medium
xy1y = x·sin x

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

∫₀1 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
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 =

Answer key

  1. 1. I = 0.594
  2. 2. I = −8.333
  3. 3. I = 6.389
  4. 4. I = 0.3012
  5. 5. A = 0.6667
  6. 6. V = 15.89

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