AP® CALCULUS AB 2006 SCORING GUIDELINES (Form B) © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 2Question 1 Let f be the function given by ()323cos .432xxxfxx=−−+ Let Rbe the shaded region in the second quadrant bounded by the graph of f, and let S be the shaded region bounded by the graph of f and line ,lthe line tangent to the graph of f at 0,x= as shown above. (a) Find the area of R. (b) Find the volume of the solid generated when R is rotated about the horizontal line 2.y=−(c) Write, but do not evaluate, an integral expression that can be used to find the area of S. For 0,x<()0fx= when 1.37312.x=−Let 1.37312.P=−(a) Area of ()02.903PRfxdx==∫2 : {1 : integral1 : answer(b) Volume ()()()0224 59.361Pfxdxπ=+−=∫4 : 1 : limits and constant 2 : integrand 1 : answer⎧⎪⎨⎪⎩(c) The equation of the tangent line l is 13.2yx=− The graph of f and line l intersect at 3.38987.A= Area of ()()()0132ASxfxdx=−−⌠⎮⌡3 : 1 : tangent line1 : integrand 1 : limits⎧⎪⎨⎪⎩
© 2006 The College Board. All rights reserved.Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents).
© 2006 The College Board. All rights reserved.Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents).
© 2006 The College Board. All rights reserved.Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents).
© 2006 The College Board. All rights reserved.Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents).
© 2006 The College Board. All rights reserved.Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents).
