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
xy01

Evaluate I = ∫01 (x3 + 4x + 6) dx.

f(x) = x3 + 4x + 6[0, 1]
I =
2.Easy
xy3y = √(x)

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

y = √(x)0 ≤ x ≤ 3
V =
3.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)1 dx.

f(x) = 2x·(x² + 1)1[0, 2]
I =
4.Medium
xy02

Evaluate I = ∫02 e2x dx.

f(x) = e2x[0, 2]
I =
5.Hard
xyy = x2​y = 2x

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

y = x2y = 2x
A =
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 = 8.25
  2. 2. V = 14.14
  3. 3. I = 12
  4. 4. I = 26.8
  5. 5. A = 1.333
  6. 6. A = 2.667

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