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
xy02

Evaluate I = ∫02 (4x3 + 6x + 1) dx.

f(x) = 4x3 + 6x + 1[0, 2]
I =
2.Easy
xy02

Evaluate I = ∫02 (3x3 + 5x − 4) dx.

f(x) = 3x3 + 5x − 4[0, 2]
I =
3.Medium
xy16y = x ln x

Evaluate I = ∫₁6 x·ln x dx.

∫₁6 x ln x dx
I =
4.Medium
xy3y = 3x

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

y = 3x0 ≤ x ≤ 3
V =
5.Hard
xy−11

Find the area A of the region between the parabola y = 1 − x² and the x-axis.

y = 1 − x²
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 = 30
  2. 2. I = 14
  3. 3. I = 23.5
  4. 4. V = 254.5
  5. 5. A = 1.333
  6. 6. A = 2.667

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