Area bounded between two curves, choosing curves

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SUMMARY

When calculating the area bounded between two curves, the choice of which curve to designate as g(x) in the integral S[f(x)-g(x)]dx is not critical, as the results will only differ by a negative sign. The integral can be evaluated regardless of the order of subtraction, and the absolute value of the result can be taken to ensure a positive area. This insight simplifies the process of determining the area between curves, making it less intuitive but more straightforward.

PREREQUISITES
  • Understanding of integral calculus, specifically definite integrals.
  • Familiarity with functions and their graphical representations.
  • Knowledge of the concept of bounded areas between curves.
  • Basic skills in manipulating algebraic expressions.
NEXT STEPS
  • Study the properties of definite integrals and their applications in area calculations.
  • Explore graphical methods for identifying intersections of curves.
  • Learn about the implications of absolute values in integral results.
  • Practice solving problems involving area between curves using various functions.
USEFUL FOR

Students in calculus courses, educators teaching integral calculus, and anyone interested in mastering the calculation of areas between curves in mathematical analysis.

JesseJC
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I don't have a particular problem in mind here, so please move this thread if it's in the wrong section.

I was wondering, when you're trying to find the area bounded between two curves, is there a foolproof way to choose which curve to be g(x) in (let S be the integral sign, haha) S[f(x)-g(x)]dx? Is there a way to tell by looking at the graph?

I've done a few of these problems and choosing which curve to subtract is not always intuitive, to me at least.
 
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JesseJC said:
I don't have a particular problem in mind here, so please move this thread if it's in the wrong section.

I was wondering, when you're trying to find the area bounded between two curves, is there a foolproof way to choose which curve to be g(x) in (let S be the integral sign, haha) S[f(x)-g(x)]dx? Is there a way to tell by looking at the graph?

I've done a few of these problems and choosing which curve to subtract is not always intuitive, to me at least.
It really doesn't matter - the two answers that you'll obtain will only differ by a minus sign. Just take the modulus of the answer either way.
 

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