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 (−3x³ − 3x + 6) dx.

f(x) = −3x³ − 3x + 6[0, 3]

I =

2.Easy

The region under y = √(x) from x = 0 to x = 4 is rotated about the x-axis. Find the volume V of the solid (a paraboloid).

y = √(x)0 ≤ x ≤ 4

V =

3.Medium

Evaluate I = ∫₀^π/2 x·sin x dx (x in radians).

∫₀^π/2 x·sin x dx

I =

4.Medium

Evaluate I = ∫₀³ e^0.5x dx.

f(x) = e^0.5x[0, 3]

I =

5.Hard

Find the area A of the region enclosed by y = x² and y = 3x.

y = x²y = 3x

A =

6.Hard

The region between the line y = 5x and the parabola y = 3x² is rotated about the x-axis. Find the volume V of the solid.

y = 5xy = 3x²

V =

Answer key

1. I = −56.25
2. V = 25.13
3. I = 1
4. I = 6.963
5. A = 4.5
6. V = 48.48

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