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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 ?
• The value in kg/hour mean how many kg are produced per hour. Since it is the derivative, it just shows how much the amount of ketchup is growing, at that instant, with respect to time.
(1 vote)
• 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?