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
xy14

Evaluate I = ∫14 (x3 − 4x − 3) dx.

f(x) = x3 − 4x − 3[1, 4]
I =
2.Easy
xy01

Evaluate I = ∫01 (−x2 − 4x + 5) dx.

f(x) = −x2 − 4x + 5[0, 1]
I =
3.Medium
xyπ/3y = x·sin x

Evaluate I = ∫₀π/3 x·sin x dx (x in radians).

∫₀π/3 x·sin x dx
I =
4.Medium
xy3y = √(2x)

The region under y = √(2x) from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(2x)0 ≤ x ≤ 3
V =
5.Hard
xy3y = 3xy = x²

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

y = 3xy = x²
V =
6.Hard
xyy = 2x2​y = 4x

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

y = 2x2y = 4x
A =

Answer key

  1. 1. I = 24.75
  2. 2. I = 2.667
  3. 3. I = 0.3424
  4. 4. V = 28.27
  5. 5. V = 101.8
  6. 6. A = 2.667

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