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
xy12

Evaluate I = ∫12 (−x3 + 4x + 5) dx.

f(x) = −x3 + 4x + 5[1, 2]
I =
3.Medium
xy1y = x·cos x

Evaluate I = ∫₀1 x·cos x dx (x in radians).

∫₀1 x·cos x dx
I =
4.Medium
xy15y = x ln x

Evaluate I = ∫₁5 x·ln x dx.

∫₁5 x ln x dx
I =
5.Hard
xy1.5y = 3xy = 2x²

The region between the line y = 3x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 3xy = 2x²
V =
6.Hard
xy1.5y = x²eˣ

Evaluate I = ∫₀1.5 x²·eˣ dx.

∫₀1.5 x²eˣ dx
I =

Answer key

  1. 1. I = 4
  2. 2. I = 7.25
  3. 3. I = 0.3818
  4. 4. I = 14.12
  5. 5. V = 12.72
  6. 6. I = 3.602

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