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
xy1y = xex​

Evaluate I = ∫₀1 x·ex dx.

∫₀1 x·ex dx
I =
2.Easy
xy−11

Evaluate I = ∫−11 (3x3 + 2x + 8) dx.

f(x) = 3x3 + 2x + 8[−1, 1]
I =
3.Medium
xyπy = x·sin x

Evaluate I = ∫₀π x·sin x dx (x in radians).

∫₀π x·sin x dx
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 cone).

y = x0 ≤ x ≤ 1
V =
5.Hard
xy−11

Find the area A of the region between the parabola y = 1 − x² and the x-axis.

y = 1 − x²
A =
6.Hard
xy−22

Find the area A of the region between the parabola y = 4 − x² and the x-axis.

y = 4 − x²
A =

Answer key

  1. 1. I = 1
  2. 2. I = 16
  3. 3. I = 3.142
  4. 4. V = 1.047
  5. 5. A = 1.333
  6. 6. A = 10.67

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