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
xy1y = xex​

Evaluate I = ∫₀1 x·ex dx.

∫₀1 x·ex dx
I =
2.Easy
xy−10

Evaluate I = ∫−10 (−x3 + 3x − 2) dx.

f(x) = −x3 + 3x − 2[−1, 0]
I =
3.Medium
xy26

Evaluate I = ∫26 2/x dx.

f(x) = 2/x[2, 6]
I =
4.Medium
xy2y = √(x)

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

y = √(x)0 ≤ x ≤ 2
V =
5.Hard
xyy = 2x2​y = 3x

Find the area A of the region enclosed by y = 2x2 and y = 3x.

y = 2x2y = 3x
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 = 1
  2. 2. I = −3.25
  3. 3. I = 2.197
  4. 4. V = 6.283
  5. 5. A = 1.125
  6. 6. A = 2.667

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