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# Jeffrey Santos - PowerPoint PPT Presentation

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

AP Calculus FRQ

Year 2008

#5

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:

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

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

Part C. Continued can be used to find the volume of the solid generated when R is rotated about the y-axis.

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

Any Questions?! can be used to find the volume of the solid generated when R is rotated about the y-axis.

Citations: can be used to find the volume of the solid generated when R is rotated about the y-axis.

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