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 = ∫₀^2.5 x·e^−x dx.

∫₀^2.5 x·e^−x dx

I =

2.Easy

Evaluate I = ∫₁⁴ (−3x³ + 6x) dx.

f(x) = −3x³ + 6x[1, 4]

I =

3.Medium

Evaluate I = ∫₁⁴ x·ln x dx.

∫₁⁴ x ln x dx

I =

4.Medium

Evaluate I = ∫₀³ e^0.5x dx.

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

I =

5.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 =

6.Hard

Find the area A of the region enclosed by y = 0.5x² and y = 2x.

y = 0.5x²y = 2x

A =

Answer key

1. I = 0.7127
2. I = −146.3
3. I = 7.34
4. I = 6.963
5. V = 107.2
6. A = 5.333

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