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

Evaluate I = ∫₀³ (−2x² − 4x + 5) dx.

f(x) = −2x² − 4x + 5[0, 3]

I =

2.Easy

Evaluate I = ∫₀³ x·e^x/2 dx.

∫₀³ x·e^x/2 dx

I =

3.Medium

Evaluate I = ∫₂⁴ 5/x dx.

f(x) = 5/x[2, 4]

I =

4.Medium

The region under y = 2x from x = 0 to x = 2 is rotated about the x-axis. Find the volume V of the solid (a cone).

y = 2x0 ≤ x ≤ 2

V =

5.Hard

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

y = 1 − x²

A =

6.Hard

The region between the line y = 3x and the parabola y = 2x² is rotated about the x-axis. Find the volume V of the solid.

y = 3xy = 2x²

V =

Answer key

1. I = −21
2. I = 12.96
3. I = 3.466
4. V = 33.51
5. A = 1.333
6. V = 12.72

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