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 = ∫₀² x·e^x/2 dx.

∫₀² x·e^x/2 dx

I =

2.Easy

Evaluate I = ∫₀¹ (−4x³ − 6x − 5) dx.

f(x) = −4x³ − 6x − 5[0, 1]

I =

3.Medium

The region under y = √(2x) from x = 0 to x = 1 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(2x)0 ≤ x ≤ 1

V =

4.Medium

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

∫₀^π/3 x·sin x dx

I =

5.Hard

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

y = 2xy = x²

V =

6.Hard

Find the area A of the region enclosed by y = 0.5x² and y = 4x.

y = 0.5x²y = 4x

A =

Answer key

1. I = 4
2. I = −9
3. V = 3.142
4. I = 0.3424
5. V = 13.4
6. A = 42.67

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