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

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 paraboloid).

y = √(2x)0 ≤ x ≤ 2

V =

2.Easy

Evaluate I = ∫₀² (2x³ + x) dx.

f(x) = 2x³ + x[0, 2]

I =

3.Medium

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

∫₀^π/3 x·sin x dx

I =

4.Medium

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

∫₀^π/3 x·cos x dx

I =

5.Hard

Find the area A of the region enclosed by y = x² and y = 4x.

y = x²y = 4x

A =

6.Hard

The region between the line y = 2x and the parabola y = 0.5x² is rotated about the x-axis. Find the volume V of the solid.

y = 2xy = 0.5x²

V =

Answer key

1. V = 12.57
2. I = 10
3. I = 0.3424
4. I = 0.4069
5. A = 10.67
6. V = 107.2

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