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
xy13

Evaluate I = ∫13 (4x2 + 3x + 3) dx.

f(x) = 4x2 + 3x + 3[1, 3]
I =
2.Easy
xy01

Evaluate I = ∫01 (−4x3 − 6x) dx.

f(x) = −4x3 − 6x[0, 1]
I =
3.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)2 dx.

f(x) = 2x·(x² + 1)2[0, 1]
I =
4.Medium
xy1y = √(x)

The region under y = √(x) from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(x)0 ≤ x ≤ 1
V =
5.Hard
xy3y = x²eˣ

Evaluate I = ∫₀3 x²·eˣ dx.

∫₀3 x²eˣ dx
I =
6.Hard
xy2.5y = x²eˣ

Evaluate I = ∫₀2.5 x²·eˣ dx.

∫₀2.5 x²eˣ dx
I =

Answer key

  1. 1. I = 52.67
  2. 2. I = −4
  3. 3. I = 2.333
  4. 4. V = 1.571
  5. 5. I = 98.43
  6. 6. I = 37.59

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