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 = √(4x)

The region under y = √(4x) from x = 0 to x = 3 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(4x)0 ≤ x ≤ 3
V =
2.Easy
xy−21

Evaluate I = ∫−21 (3x2 − 2x + 2) dx.

f(x) = 3x2 − 2x + 2[−2, 1]
I =
3.Medium
xyπ/2y = x·cos x

Evaluate I = ∫₀π/2 x·cos x dx (x in radians).

∫₀π/2 x·cos x dx
I =
4.Medium
xy14y = x ln x

Evaluate I = ∫₁4 x·ln x dx.

∫₁4 x ln x dx
I =
5.Hard
xy−33

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

y = 9 − x²
A =
6.Hard
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =

Answer key

  1. 1. V = 56.55
  2. 2. I = 18
  3. 3. I = 0.5708
  4. 4. I = 7.34
  5. 5. A = 36
  6. 6. I = 12.78

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