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
xy−11

Evaluate I = ∫−11 (4x3 − 2x − 1) dx.

f(x) = 4x3 − 2x − 1[−1, 1]
I =
2.Easy
xy3y = xe2x​

Evaluate I = ∫₀3 x·e2x dx.

∫₀3 x·e2x dx
I =
3.Medium
xyπ/3y = x·cos x

Evaluate I = ∫₀π/3 x·cos x dx (x in radians).

∫₀π/3 x·cos x dx
I =
4.Medium
xy12

Evaluate I = ∫12 5/x dx.

f(x) = 5/x[1, 2]
I =
5.Hard
xyy = x2​y = 2x

Find the area A of the region enclosed by y = x2 and y = 2x.

y = x2y = 2x
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 = −2
  2. 2. I = 504.5
  3. 3. I = 0.4069
  4. 4. I = 3.466
  5. 5. A = 1.333
  6. 6. A = 10.67

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