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Jeffrey Santos

Jeffrey Santos. AP Calculus FRQ Year 2008 #5. The Question?. A.) Find the Area of R. Using the graphing calculator, we find the intersection points of y=lnx and y=x-2. The intersection points of the graph are when x=.15859 and 3.14619. (Let A=.15859 and B=3.14619). Which then equals to:.

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Jeffrey Santos

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  1. Jeffrey Santos AP Calculus FRQ Year 2008 #5

  2. The Question?

  3. A.) Find the Area of R • Using the graphingcalculator, we find the intersection points of y=lnx and y=x-2 The intersection points of the graph are when x=.15859 and 3.14619. (Let A=.15859 and B=3.14619) Which then equals to: To find the area of R, we do: 1.949 Plug in the formula to get:

  4. B.) Find the volume of the solid generated when R isrotated about the horizontal line y=-3 • Using the washer method, (since there two functions) from point A to B we get: Use graphing calculator and you get: 34.199

  5. C.) Write, but do not evaluate, and integral expression that can be used to find the volume of the solid generated when R is rotated about the y-axis. • Since it is rotated over the y-axis, we set both functions equal to X in terms of Y. • Y=ln(x) becomes • Y=X-2 becomes The new graph has two new intersection points, which are: Where x=1.1461 Where X= -1.8414

  6. Part C. Continued We plug it back into the Washer Method formula. • With the new intersection points: x=1.1461(D) and -1.8414 (C). And the new functions: We then get the formula: and

  7. Any Questions?!

  8. Citations: • http://apcentral.collegeboard.com/apc/public/repository/_ap06_frq_calculusab_51707.pdf for the problem.

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