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 = √(x)

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

y = √(x)0 ≤ x ≤ 4
V =
2.Easy
xy13

Evaluate I = ∫13 (−4x2 + 1) dx.

f(x) = −4x2 + 1[1, 3]
I =
3.Medium
xy1y = √(x)

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

y = √(x)0 ≤ x ≤ 1
V =
4.Medium
xy1y = x·cos x

Evaluate I = ∫₀1 x·cos x dx (x in radians).

∫₀1 x·cos x dx
I =
5.Hard
xyy = x2​y = 4x

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

y = x2y = 4x
A =
6.Hard
xy2y = xy = 0.5x²

The region between the line y = x and the parabola y = 0.5x² is rotated about the x-axis. Find the volume V of the solid.

y = xy = 0.5x²
V =

Answer key

  1. 1. V = 25.13
  2. 2. I = −32.67
  3. 3. V = 1.571
  4. 4. I = 0.3818
  5. 5. A = 10.67
  6. 6. V = 3.351

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