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
xy1y = xex​

Evaluate I = ∫₀1 x·ex dx.

∫₀1 x·ex dx
I =
3.Medium
xy02

Evaluate I = ∫02 e−x dx.

f(x) = e−x[0, 2]
I =
4.Medium
xy15

Evaluate I = ∫15 3/x dx.

f(x) = 3/x[1, 5]
I =
5.Hard
xy1.5y = 3xy = 2x²

The region between the line y = 3x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 3xy = 2x²
V =
6.Hard
xy−22

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

y = 4 − x²
A =

Answer key

  1. 1. V = 16.76
  2. 2. I = 1
  3. 3. I = 0.8647
  4. 4. I = 4.828
  5. 5. V = 12.72
  6. 6. A = 10.67

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