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
xy−21

Evaluate I = ∫−21 (−3x3 + 3x + 7) dx.

f(x) = −3x3 + 3x + 7[−2, 1]
I =
2.Easy
xy2y = xe2x​

Evaluate I = ∫₀2 x·e2x dx.

∫₀2 x·e2x dx
I =
3.Medium
xy13y = x ln x

Evaluate I = ∫₁3 x·ln x dx.

∫₁3 x ln 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
xy4y = 2xy = 0.5x²

The region between the line y = 2x and the parabola y = 0.5x² is rotated about the x-axis. Find the volume V of the solid.

y = 2xy = 0.5x²
V =
6.Hard
xyy = 0.5x2​y = 4x

Find the area A of the region enclosed by y = 0.5x2 and y = 4x.

y = 0.5x2y = 4x
A =

Answer key

  1. 1. I = 27.75
  2. 2. I = 41.2
  3. 3. I = 2.944
  4. 4. I = 2.333
  5. 5. V = 107.2
  6. 6. A = 42.67

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