Differential Equations For Dummies
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Although differentiation helps you figure out a lot of things about a function, there's one thing that differentiation cannot answer: What's the function's average height? To answer that, you need integration.

The following practice questions ask you to find average values using integration.

Practice questions

  1. What's the average value of

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  2. A car's speed in feet per second is given by f(t) = t1.7 – 6t + 80. What's its average speed from t = 5 seconds to t = 15 seconds? What's that in miles per hour?

Answers and explanations

  1. The average value is 0.03.

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    Do this with a u-substitution.

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  2. The car's average speed is about 72.62 feet per second, or 49.51 miles per hour.

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About This Article

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Steven Holzner was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.

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