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
xy01

Evaluate I = ∫01 (−4x2 − x + 4) dx.

f(x) = −4x2 − x + 4[0, 1]
I =
2.Easy
xy03

Evaluate I = ∫03 (−x3 + 5x − 2) dx.

f(x) = −x3 + 5x − 2[0, 3]
I =
3.Medium
xy01

Evaluate I = ∫01 2x·(x² + 1)3 dx.

f(x) = 2x·(x² + 1)3[0, 1]
I =
4.Medium
xy1y = x·cos x

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

∫₀1 x·cos x dx
I =
5.Hard
xy2y = x²eˣ

Evaluate I = ∫₀2 x²·eˣ dx.

∫₀2 x²eˣ dx
I =
6.Hard
xy3y = 6xy = 2x²

The region between the line y = 6x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 6xy = 2x²
V =

Answer key

  1. 1. I = 2.167
  2. 2. I = −3.75
  3. 3. I = 3.75
  4. 4. I = 0.3818
  5. 5. I = 12.78
  6. 6. V = 407.2

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