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−12

Evaluate I = ∫−12 (2x3 − 5x + 1) dx.

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

Evaluate I = ∫₀1.5 x·ex dx.

∫₀1.5 x·ex dx
I =
3.Medium
xy210

Evaluate I = ∫210 1/x dx.

f(x) = 1/x[2, 10]
I =
4.Medium
xy1y = 2x

The region under y = 2x from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 2x0 ≤ x ≤ 1
V =
5.Hard
xyy = 0.5x2​y = 2x

Find the area A of the region enclosed by y = 0.5x2 and y = 2x.

y = 0.5x2y = 2x
A =
6.Hard
xy2.5y = 5xy = 2x²

The region between the line y = 5x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 5xy = 2x²
V =

Answer key

  1. 1. I = 3
  2. 2. I = 3.241
  3. 3. I = 1.609
  4. 4. V = 4.189
  5. 5. A = 5.333
  6. 6. V = 163.6

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