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### Course: AP®︎/College Calculus AB>Unit 8

Lesson 3: Using accumulation functions and definite integrals in applied contexts

# Worked examples: interpreting definite integrals in context

Interpreting expressions involving definite integrals in a real-world context.

## Want to join the conversation?

• Why would we use integrals to represent Julia's revenue? Isn't that unnecessarily complicated?
• I think integrals allow us to see the accumulation of her revenue at a certain interval of time.
• what would the definite integral of just k(t) from 0-4 be measuring? Its units would be kg*s.
• The owner of the sauce factory might charge a potential competitor who doesn't have a factory—perhaps because they are just starting out in the business—a usage fee of \$1 per hour per kilogram of ketchup produced. The definite integral of k(t) from 0 to 4 would then measure the total fee for those four hours.
• For the ketchap problem, what happens if we take the integral to K(t) rather than K'(t). We will get something Kg hours. What does this means ?
• Are the domains of k'(t) discrete in the second problem? Since t is in hours, would t have to be integers only or does it take any real number as its domain?