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
xy4y = 0.5x

The region under y = 0.5x from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 4
V =
2.Easy
xy3y = xex​

Evaluate I = ∫₀3 x·ex dx.

∫₀3 x·ex dx
I =
3.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 cone).

y = 2x0 ≤ x ≤ 1
V =
4.Medium
xy12y = x ln x

Evaluate I = ∫₁2 x·ln x dx.

∫₁2 x ln x dx
I =
5.Hard
xyy = 0.5x2​y = 4x

Find the area A of the region enclosed by y = 0.5x2 and y = 4x.

y = 0.5x2y = 4x
A =
6.Hard
xy−11

Find the area A of the region between the parabola y = 1 − x² and the x-axis.

y = 1 − x²
A =

Answer key

  1. 1. V = 16.76
  2. 2. I = 41.17
  3. 3. V = 4.189
  4. 4. I = 0.6363
  5. 5. A = 42.67
  6. 6. A = 1.333

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