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

  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.


    Do this with a u-substitution.

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


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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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