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The Net Change Theorem, Slides of Calculus

Texas A&M University (A&M)Calculus

Express the product as a difference and then you can integrate each term. The Net Change Theorem. The integral of a rate of change is the net change in.

Typology: Slides

2022/2023

Uploaded on 03/01/2023

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HomeworkQuestions.TheintegralofaproductisNOT
theproductoftheintegrals,soyouneedtodistributefirst.
Expresstheproductasadifferenceandthenyoucan
integrateeachterm.
The Net Change Theorem
The integral of a rate of change is the net change in
the function F:
∫
F'(x) dx = F(b) - F(a)
a
b
pf3
pf4

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Homework Questions. The integral of a product is NOT

the product of the integrals, so you need to distribute first.

Express the product as a difference and then you can

integrate each term.

The Net Change Theorem

The integral of a rate of change is the net change in

the function F:

∫ a F'(x)^ dx^ =^ F(b)^ -^ F(a)

b

EXAMPLE: Suppose that p'(t) represents the rate at which the population of a county

increases, in people per year, starting in 1990.

Then what does the following integral represent?

∫ p'(t)^ dt

Consider y = 4 and y = x^2 from x = 0 to x = 2. What if we elect to use horizontal slices...

Find the total distance traveled by the particle in the first 4 seconds. The velocity of a particle, in cm/sec, moving along a straight path is given by The velocity is not always above the axis so we must figure out where it drops below. Change the sign so that the negative area turns positive. To account for all distance, we are really thinking about integrating using the absolute value of the velocity function. We have to take a look at the function and force the sign changes.

Total Distance =