What is the Solution to a Challenging Integration Homework Problem?

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SUMMARY

The discussion centers on a challenging integration homework problem involving a function f that passes through the points (5, 13) and (11, 6) and is decreasing. Participants emphasize the importance of sketching the graph of f to visualize the area under the curve, which represents the integral. Additionally, the inverse function f-1 is introduced, highlighting that it swaps the x and y coordinates, necessitating a comparison of the areas between the curve and the y-axis.

PREREQUISITES
  • Understanding of integral calculus and area under curves
  • Familiarity with function graphs and their properties
  • Knowledge of inverse functions and their graphical representations
  • Basic skills in sketching mathematical functions
NEXT STEPS
  • Study the properties of decreasing functions and their integrals
  • Learn how to sketch graphs of functions based on given points
  • Explore the concept of inverse functions in detail
  • Research techniques for calculating areas under curves using integrals
USEFUL FOR

Students in calculus courses, educators teaching integration concepts, and anyone seeking to improve their understanding of function behavior and area calculations in mathematics.

MillerL7
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I attached just one question...My tutor and the TA could not figure it out or help me get started on it...can someone help me get started? Thank you so much!
 

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First Please type the problem in rather that posting a "word" file. It's not that difficult and many people won't open a "word" attachement for fear of viruses. I wouldn't if I didn't have very strong virus protection.

As for the problem itself, Draw a picture. While you don't know the exact "form" of f, you know that it passes through the points (5, 13) and (11, 6) and is decreasing so you can sketch a possible graph for f. You also know that the integral given is the area under that curve- the area between that curve and the x-axis. Draw the boundaries of that region.

Now, f-1 just "swaps" x and y so the integral of f-1 you are looking for is the area between that curve and the y- axis. Draw the boundaries and conpare the two areas.
 

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