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Finding the area between the curves

Finding the area between the curves. Karla Kirsch Period 5/6. THE QUESTION. a) Find the area of R. In order to find the area of R, you need to… Figure out which equation is the top and which one is the bottom Find out the interval of the figure Integrate the function using top minus bottom

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Finding the area between the curves

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  1. Finding the area between the curves Karla Kirsch Period 5/6

  2. THE QUESTION

  3. a) Find the area of R. • In order to find the area of R, you need to… • Figure out which equation is the top and which one is the bottom • Find out the interval of the figure • Integrate the function using top minus bottom • Plug into the calculator and solve. Top function y=6 Bottom function y=4ln(3-x)

  4. Create the integral and plug it into the calculator Answer: R = 6.817

  5. b) Find the volume of the solid generated when R is revolved about the horizontal line y=8 • In order to find the volume of a solid you must use the equation: : • You take whatever line the solid is being revolved around, and subtract each equation from it • Plug this into the equation and plug into the calculator

  6. Plug the values into the equation and solve on the calculator • R(x)= (8-4ln(3-x)) r(x)= (8-6) Answer : V= 168.179

  7. 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. • When using cross sections, you must first identify the shape that is described in the problem; which is a square for this question. • Once you identify the shape, figure out the formula for the area of that shape. • Volume of the solid= Area between the curves, plugged into the formula for area of the cross section • V = ∫(A)² dx

  8. Plug values into the equation of volume • R=(6-4ln(3-x)) ∙∘∙∘∙ Area of square=(x)² Area of a square equation Area between the curves

  9. Plug the equation into the calculator and solve Answer : V=26.266

  10. CITATIONS • http://apcentral.collegeboard.com/apc/public/repository/ap10_calculus_ab_form_b_q1.pdf • http://www.animatedgif.net/ • http://mszhao.com/

  11. THE END ☺♥

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