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−11

Evaluate I = ∫−11 (2x2 − 3x + 5) dx.

f(x) = 2x2 − 3x + 5[−1, 1]
I =
2.Easy
xy3y = 0.5x

The region under y = 0.5x from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 0.5x0 ≤ x ≤ 3
V =
3.Medium
xy14

Evaluate I = ∫14 2/x dx.

f(x) = 2/x[1, 4]
I =
4.Medium
xyπ/2y = x·sin x

Evaluate I = ∫₀π/2 x·sin x dx (x in radians).

∫₀π/2 x·sin x dx
I =
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 = x2​y = 2x

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

y = x2y = 2x
A =

Answer key

  1. 1. I = 11.33
  2. 2. V = 7.069
  3. 3. I = 2.773
  4. 4. I = 1
  5. 5. A = 1.333
  6. 6. A = 1.333

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