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 = √(4x)

The region under y = √(4x) from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(4x)0 ≤ x ≤ 3
V =
2.Easy
xy4y = x

The region under y = x from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = x0 ≤ x ≤ 4
V =
3.Medium
xy12

Evaluate I = ∫12 2/x dx.

f(x) = 2/x[1, 2]
I =
4.Medium
xyπy = x·cos x

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

∫₀π x·cos x dx
I =
5.Hard
xy−22

Find the area A of the region between the parabola y = 4 − x² and the x-axis.

y = 4 − x²
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. V = 56.55
  2. 2. V = 67.02
  3. 3. I = 1.386
  4. 4. I = −2
  5. 5. A = 10.67
  6. 6. A = 36

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