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−2−1

Evaluate I = ∫−2−1 (−4x3 − 6x + 7) dx.

f(x) = −4x3 − 6x + 7[−2, −1]
I =
2.Easy
xy13

Evaluate I = ∫13 (4x3 + 4x + 3) dx.

f(x) = 4x3 + 4x + 3[1, 3]
I =
3.Medium
xy1y = x·cos x

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

∫₀1 x·cos x dx
I =
4.Medium
xy11.5y = x ln x

Evaluate I = ∫₁1.5 x·ln x dx.

∫₁1.5 x ln x dx
I =
5.Hard
xy1y = 2xy = 2x²

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

y = 2xy = 2x²
V =
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 = 31
  2. 2. I = 102
  3. 3. I = 0.3818
  4. 4. I = 0.1436
  5. 5. V = 1.676
  6. 6. A = 10.67

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