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
xy0.5y = xex/2​

Evaluate I = ∫₀0.5 x·ex/2 dx.

∫₀0.5 x·ex/2 dx
I =
2.Easy
xy−12

Evaluate I = ∫−12 (3x3) dx.

f(x) = 3x3[−1, 2]
I =
3.Medium
xy03

Evaluate I = ∫03 e−0.5x dx.

f(x) = e−0.5x[0, 3]
I =
4.Medium
xy4y = √(4x)

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

y = √(4x)0 ≤ x ≤ 4
V =
5.Hard
xyy = 2x2​y = 4x

Find the area A of the region enclosed by y = 2x2 and y = 4x.

y = 2x2y = 4x
A =
6.Hard
xy1y = xy = x²

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

y = xy = x²
V =

Answer key

  1. 1. I = 0.1479
  2. 2. I = 11.25
  3. 3. I = 1.554
  4. 4. V = 100.5
  5. 5. A = 2.667
  6. 6. V = 0.4189

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