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
xy−21

Evaluate I = ∫−21 (4x3 − 2x − 5) dx.

f(x) = 4x3 − 2x − 5[−2, 1]
I =
2.Easy
xy1.5y = xe−x​

Evaluate I = ∫₀1.5 x·e−x dx.

∫₀1.5 x·e−x dx
I =
3.Medium
xy14

Evaluate I = ∫14 2/x dx.

f(x) = 2/x[1, 4]
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
xy4y = 4xy = x²

The region between the line y = 4x and the parabola y = x² is rotated about the x-axis. Find the volume V of the solid.

y = 4xy = x²
V =
6.Hard
xyy = 0.5x2​y = 3x

Find the area A of the region enclosed by y = 0.5x2 and y = 3x.

y = 0.5x2y = 3x
A =

Answer key

  1. 1. I = −27
  2. 2. I = 0.4422
  3. 3. I = 2.773
  4. 4. V = 28.27
  5. 5. V = 428.9
  6. 6. A = 18

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