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 = 0.5x

The region under y = 0.5x from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 2
V =
2.Easy
xy2y = xex/2​

Evaluate I = ∫₀2 x·ex/2 dx.

∫₀2 x·ex/2 dx
I =
3.Medium
xy24

Evaluate I = ∫24 3/x dx.

f(x) = 3/x[2, 4]
I =
4.Medium
xy12.5y = x ln x

Evaluate I = ∫₁2.5 x·ln x dx.

∫₁2.5 x ln 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
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. V = 2.094
  2. 2. I = 4
  3. 3. I = 2.079
  4. 4. I = 1.551
  5. 5. A = 0.6667
  6. 6. A = 18

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