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
xy0.5y = xe−x​

Evaluate I = ∫₀0.5 x·e−x dx.

∫₀0.5 x·e−x dx
I =
2.Easy
xy−12

Evaluate I = ∫−12 (−4x3 + 3x + 1) dx.

f(x) = −4x3 + 3x + 1[−1, 2]
I =
3.Medium
xy02

Evaluate I = ∫02 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 2]
I =
4.Medium
xy13y = x ln x

Evaluate I = ∫₁3 x·ln x dx.

∫₁3 x ln x dx
I =
5.Hard
xy3y = 3xy = x²

The region between the line y = 3x and the parabola y = x² is rotated about the x-axis. Find the volume V of the solid.

y = 3xy = x²
V =
6.Hard
xyy = 0.5x2​y = x

Find the area A of the region enclosed by y = 0.5x2 and y = x.

y = 0.5x2y = x
A =

Answer key

  1. 1. I = 0.0902
  2. 2. I = −7.5
  3. 3. I = 156
  4. 4. I = 2.944
  5. 5. V = 101.8
  6. 6. A = 0.6667

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