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
xy2y = xe−x​

Evaluate I = ∫₀2 x·e−x dx.

∫₀2 x·e−x dx
I =
2.Easy
xy12

Evaluate I = ∫12 (−4x2 − 5x + 6) dx.

f(x) = −4x2 − 5x + 6[1, 2]
I =
3.Medium
xy2y = x·cos x

Evaluate I = ∫₀2 x·cos x dx (x in radians).

∫₀2 x·cos x dx
I =
4.Medium
xy15

Evaluate I = ∫15 2/x dx.

f(x) = 2/x[1, 5]
I =
5.Hard
xyy = x2​y = x

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

y = x2y = x
A =
6.Hard
xyy = 2x2​y = 2x

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

y = 2x2y = 2x
A =

Answer key

  1. 1. I = 0.594
  2. 2. I = −10.83
  3. 3. I = 0.4024
  4. 4. I = 3.219
  5. 5. A = 0.1667
  6. 6. A = 0.3333

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