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By Steven Mejia

By Steven Mejia. Area. AP Calculus Project. Volume. Cross Sections. Problem. Let R be the region in the first quadrant bounded by the graph of , the horizontal line , and the y-axis, as shown above in the figure above. Find the area of R

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By Steven Mejia

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  1. By Steven Mejia Area AP Calculus Project Volume Cross Sections

  2. Problem Let R be the region in the first quadrant bounded by the graph of , the horizontal line , and the y-axis, as shown above in the figure above. Find the area of R Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is the rotated about the horizontal line Region R is the base of the solid. For each y, where , the cross section of the solid taken perpendicular to the y-axis is a rectangle whose height is 3 time the length of its base inthe region R. Write, but do not evaluate, an integral expression that gives the volume of the solid.

  3. Part A – Analytically

  4. Part A – Calculator First, go to math. Then scroll down to fnInt (. Next, you plug in the interval, which in this case is zero and 9. After, you put in the top function, y=6, minus the bottom function, . Finally, you put dx and press enter. Your answer would be 18. Calculator to the rescue!!!

  5. Part A - Table Use the table for the antiderivative. The antiderivative is . On the table on the side, look specifically when x=0 and when x=9. Subtract the two and it will give you 18. This way rocks!!!

  6. Part B Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line 7

  7. Part D Region R is the base of a solid. For each y, where 0 ≤ y ≤ 6 the cross section of the solid taken perpendicular to the y-axis is a rectangle whose height is 3 times the length of its base in region R. Write, but do not evaluate, an integral expression that gives the volume of the solid. Area of rectangle = base x height Base= height = Area of rectangle =

  8. Citations • http://apcentral.collegeboard.com/apc/public/repository/ap10_calculus_ab_q4.pdf

  9. Any Questions? The End

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