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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

# Interpreting definite integral as net change

The definite integral of a rate function gives us the net change in the quantity described by the rate. See how we interpret definite integrals in a real-world context.

## Want to join the conversation?

• So how can we figure the area created by 2 functions like (x-1)e^6 and x^2 -1 .
(1 vote)
• Do you mean the area between the curves?

Take the integral of (x-1)e^6 -(x^2-1). If the area is negative just take the absolute value of it. Obviously you need to works out the bounds first for integral so you need find the values of x such x-1e^6 = x^2-1.
• what is the difference between rate and velocity? they both have the unit "meter per second" right?
(1 vote)
• Not necessarily. Velocity is a rate of change(of displacement, to be exact) but there are so many rates. Essentially, to say the rate of something refers to differentiating it with respect to time.
• it is a bit confusing to think of distance as an area because the unit for distance is meter, but for the area is meter^2.
(1 vote)
• I understand how that can be confusing. What I usually do to avoid getting confused is instead of thinking of the area directly as the displacement, I multiply the units of the x and y axes (area's units are not always meter^2 !), thereby getting the units of the area under the curve. In this case, since this unit is the same as the unit of distance, the area under the curve represents length.

• What does the integral of acceleration represent?
(1 vote)
• Integrating acceleration gives velocity.
(1 vote)
• We must understand English language before choosing a choice. A,B,C or D.
.
Why did not Eden's rate increase by 6 kilometers per hour between the 2 and the 3 hours ? I think `the choice D` was correct ! why was the `choice C` correct with the the phrase during the third hours ? I think she came from the 2 hours to the 3 hours was correct, not during the third hours !