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
xy3y = xe2x​

Evaluate I = ∫₀3 x·e2x dx.

∫₀3 x·e2x dx
I =
2.Easy
xy2.5y = xe−x​

Evaluate I = ∫₀2.5 x·e−x dx.

∫₀2.5 x·e−x dx
I =
3.Medium
xy02

Evaluate I = ∫02 e2x dx.

f(x) = e2x[0, 2]
I =
4.Medium
xyπ/3y = x·cos x

Evaluate I = ∫₀π/3 x·cos x dx (x in radians).

∫₀π/3 x·cos 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
xy−33

Find the area A of the region between the parabola y = 9 − x² and the x-axis.

y = 9 − x²
A =

Answer key

  1. 1. I = 504.5
  2. 2. I = 0.7127
  3. 3. I = 26.8
  4. 4. I = 0.4069
  5. 5. A = 0.6667
  6. 6. A = 36

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