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 = xex/2​

Evaluate I = ∫₀2 x·ex/2 dx.

∫₀2 x·ex/2 dx
I =
2.Easy
xy−11

Evaluate I = ∫−11 (3x2 − 6x + 8) dx.

f(x) = 3x2 − 6x + 8[−1, 1]
I =
3.Medium
xyπy = x·sin x

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

∫₀π x·sin x dx
I =
4.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 1]
I =
5.Hard
xy2.5y = x²eˣ

Evaluate I = ∫₀2.5 x²·eˣ dx.

∫₀2.5 x²eˣ dx
I =
6.Hard
xy−22

Find the area A of the region between the parabola y = 4 − x² and the x-axis.

y = 4 − x²
A =

Answer key

  1. 1. I = 4
  2. 2. I = 18
  3. 3. I = 3.142
  4. 4. I = 2.333
  5. 5. I = 37.59
  6. 6. A = 10.67

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