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

y = √(x)0 ≤ x ≤ 2

V =

2.Easy

Evaluate I = ∫₀^0.5 x·e^x/2 dx.

∫₀^0.5 x·e^x/2 dx

I =

3.Medium

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

∫₀¹ x·sin x dx

I =

4.Medium

Evaluate I = ∫₀² e^0.5x dx.

f(x) = e^0.5x[0, 2]

I =

5.Hard

Find the area A of the region enclosed by y = 2x² and y = 3x.

y = 2x²y = 3x

A =

6.Hard

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

y = 1 − x²

A =

Answer key

1. V = 6.283
2. I = 0.1479
3. I = 0.3012
4. I = 3.437
5. A = 1.125
6. A = 1.333

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