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 = xe2x​

Evaluate I = ∫₀3 x·e2x dx.

∫₀3 x·e2x dx
I =
2.Easy
xy01

Evaluate I = ∫01 (−4x2 + 5) dx.

f(x) = −4x2 + 5[0, 1]
I =
3.Medium
xy14y = x ln x

Evaluate I = ∫₁4 x·ln x dx.

∫₁4 x ln x dx
I =
4.Medium
xy2y = x·sin x

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

∫₀2 x·sin x dx
I =
5.Hard
xyy = 2x2​y = 4x

Find the area A of the region enclosed by y = 2x2 and y = 4x.

y = 2x2y = 4x
A =
6.Hard
xy−33

Find the area A of the region between the parabola y = 9 − x² and the x-axis.

y = 9 − x²
A =

Answer key

  1. 1. I = 504.5
  2. 2. I = 3.667
  3. 3. I = 7.34
  4. 4. I = 1.742
  5. 5. A = 2.667
  6. 6. A = 36

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