- #1

Kahing

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Hello, I am currently studying previous AP Calculus AB exams and I was wondering if someone could explain how to solve the following as clearly as possible so I have a better understanding of these problems in hope to prepare my for the exam next month.

R is the shaded region in the Figure in the first quadrant bounded by the graph of y = 4ln(3-x), the horizontal line is y = 6, and the vertical line is x = 2

a) Find the Area of R

*I have tried using the formula A = integration of a to b, [f(x) - g(x)] dx

but my answer does not come out to be 6.816 or 6.817

b) Find the volume of the solid generated when R is revolved around the horizontal line y = 8

*I have tried the Disk and Washer Methods, but still no luck, I may possibly be doing it wrong since my teacher has not explained this chapter to my class yet. The answer for b) is 26.266

c) The Region R is the base of a solid. For this solid, each cross section perpendicular to the X-axis is a square, find the volume of the solid.

The source below has a picture and official pdf file from collegeboard.org if you need a visual/ clearer explanation.

Source: [COLLEGEBOARD] http://apcentral.collegeboard.com/apc/pu…

*I Am not asking for anyone to do my homework, passing the AP exam is self motivation, and please, do not post anything unless it is helpful. Being in Calculus, I'd assume the students are not lazy to do the homework by themselves since math is built upon foundations upon foundations, its just a matter of understanding. Thank you everyone.

R is the shaded region in the Figure in the first quadrant bounded by the graph of y = 4ln(3-x), the horizontal line is y = 6, and the vertical line is x = 2

a) Find the Area of R

*I have tried using the formula A = integration of a to b, [f(x) - g(x)] dx

but my answer does not come out to be 6.816 or 6.817

b) Find the volume of the solid generated when R is revolved around the horizontal line y = 8

*I have tried the Disk and Washer Methods, but still no luck, I may possibly be doing it wrong since my teacher has not explained this chapter to my class yet. The answer for b) is 26.266

c) The Region R is the base of a solid. For this solid, each cross section perpendicular to the X-axis is a square, find the volume of the solid.

The source below has a picture and official pdf file from collegeboard.org if you need a visual/ clearer explanation.

Source: [COLLEGEBOARD] http://apcentral.collegeboard.com/apc/pu…

*I Am not asking for anyone to do my homework, passing the AP exam is self motivation, and please, do not post anything unless it is helpful. Being in Calculus, I'd assume the students are not lazy to do the homework by themselves since math is built upon foundations upon foundations, its just a matter of understanding. Thank you everyone.

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