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## AP®︎/College Calculus BC

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

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

# Analyzing problems involving definite integrals

See worked example of how to find the appropriate expression to use in order to solve word problems using definite integrals.

## Want to join the conversation?

• How did they even get 1200? if you plug in 2 for t in the function you get 546.6356401
• The function r(t) gives the RATE at which the population grows, not the actual population. Does this help?
• Why can't you do the integral from 0 to 7?
• Because he's asking us about the actual value of the population at t = 7 and not the net change in population from t = 0 to t = 7. To get the actual value of the population, we would add the change in population to the initial population. This is known as the Fundamental Theorem of Calculus (alternate form)

Using the Fundamental Theorem of Calculus (alternate form), we know that f(b) = f(a) + ∫ₐᵇ f(x) dx.

So, if we want to get r(7), we would do r(7) = r(2) + ∫₂⁷r(t) dt
=>
r(7) = 1,200 + ∫₂⁷r(t) dt

Takeaways: