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 = 3x

The region under y = 3x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 3x0 ≤ x ≤ 1
V =
2.Easy
xy03

Evaluate I = ∫03 (2x2 + 2x) dx.

f(x) = 2x2 + 2x[0, 3]
I =
3.Medium
xy16y = x ln x

Evaluate I = ∫₁6 x·ln x dx.

∫₁6 x ln x dx
I =
4.Medium
xy1y = √(2x)

The region under y = √(2x) from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(2x)0 ≤ x ≤ 1
V =
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
xyy = x2​y = x

Find the area A of the region enclosed by y = x2 and y = x.

y = x2y = x
A =

Answer key

  1. 1. V = 9.425
  2. 2. I = 27
  3. 3. I = 23.5
  4. 4. V = 3.142
  5. 5. A = 10.67
  6. 6. A = 0.1667

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