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
xy2.5y = xe−x​

Evaluate I = ∫₀2.5 x·e−x dx.

∫₀2.5 x·e−x dx
I =
2.Easy
xy01

Evaluate I = ∫01 (−x2 − 3) dx.

f(x) = −x2 − 3[0, 1]
I =
3.Medium
xy24

Evaluate I = ∫24 5/x dx.

f(x) = 5/x[2, 4]
I =
4.Medium
xyπy = x·sin x

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

∫₀π x·sin x dx
I =
5.Hard
xyy = x2​y = 4x

Find the area A of the region enclosed by y = x2 and y = 4x.

y = x2y = 4x
A =
6.Hard
xy1y = x²eˣ

Evaluate I = ∫₀1 x²·eˣ dx.

∫₀1 x²eˣ dx
I =

Answer key

  1. 1. I = 0.7127
  2. 2. I = −3.333
  3. 3. I = 3.466
  4. 4. I = 3.142
  5. 5. A = 10.67
  6. 6. I = 0.7183

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