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
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 cone).

y = 2x0 ≤ x ≤ 3
V =
2.Easy
xy−12

Evaluate I = ∫−12 (−2x3 − 5x + 4) dx.

f(x) = −2x3 − 5x + 4[−1, 2]
I =
3.Medium
xy01

Evaluate I = ∫01 e2x dx.

f(x) = e2x[0, 1]
I =
4.Medium
xy26

Evaluate I = ∫26 3/x dx.

f(x) = 3/x[2, 6]
I =
5.Hard
xy3y = 6xy = 2x²

The region between the line y = 6x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 6xy = 2x²
V =
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. V = 113.1
  2. 2. I = −3
  3. 3. I = 3.195
  4. 4. I = 3.296
  5. 5. V = 407.2
  6. 6. A = 1.333

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