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True-False Determine whether the statement is true or false. Explain your answer. [In each exercise, assume that $f$and $g$ are distinct continuous functions on $[a, b]$ and that $A$ de-notes the area of the region bounded by the graphs of $y=f(x),$$y=g(x), x=a, \text { and } x=b .]$

If$$\int_{a}^{b}[f(x)-g(x)] d x=-3$$$$\text { then } A=3$$

$$\text { False }$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 6

APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING

Section 1

Area Between Two Curves

Integrals

Integration

Applications of Integration

Area Between Curves

Volume

Arc Length and Surface Area

Missouri State University

Campbell University

University of Nottingham

Boston College

Lectures

01:11

In mathematics, integratio…

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01:58

True-False Determine wheth…

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01:28

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True, sometimes true, or n…

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04:03

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depending on the author's intentions here, I would say that this statement is false. Um, and the reason why is let's say you had some function that, um maybe, you know, look, something like this on, like, this is your ex values a And this is your xlu be. And you accidentally did this about this function minus this function, then you'll definitely get a negative answer. And so you could then say OK, well, if the area I got was negative, something went wrong. So because area needs to be positive, you take the absolute value. You get the right answer. Now, this example I just showed you would make it a true statement because the example they give us negative three. If you have value that, absolutely, you get positive. Three. The issue, though, and why I'm committing my answer to false is what if the function looks something more like this trying to make it kind of obnoxious. Here where, um, you did this function minus this? Um, the issue with that statement go is some of this, like this area would cancel out with some of this area. Um, so, like, right here, like the white space I have leftover might be an area of negative three. Um, so just absolute valuing. That is not going to be good enough. Um, is ah, incorrect. And hopefully have explained this in a good enough way. Um, I don't confuse you any more if I have, um, I would direct you to a teacher. Another student if, uh, if you still have questions.

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