Question

DO ALL PARTS PLEASE

Let f and g be the functions defined by f(x) = 1 +x+7-24 and g(x) = x* -6.572 +6x + 2. Let R and S be the two regions enclosed by the graphs off and g shown in the figure above. (a) Find the sum of the areas of regions R and S. (b) Region S is the line of a solid whose cross sections perpendicular to the x-axis are squares. Find the volume of the solid. (e) Leth be the vertical distance between the graphs off and g in region S. Find the rate at which h changes with respect to x when x = 1.8. (d/ Region R is the base of a solid whose cross sections perpendicular to the x-axis are semi-circles. Find the volume of the solid.

Answer 1

(a feng=1+ x + x² - 2x gen) = n²-6.5x² +64 +2 Let the sum of Aran be ARTS A 6,) 1.03 RS 79 - A ) de to 6.5x² - 6x + 2) Citate de 24+5x6.5x2 + 2 + en -2n) du. TR= 2076 2.09565 so s (few-gen, da Sitz reklsa) - (24.65*2 *6*2)be v ar ****52-54-) de s = 649 to 1.0009 A RTS = 2.0965 +1.0069. A - 3.1034 I

( volume of da denent Side length of each 7 3 dr = (fen-gen] 2 dn. Total volume of solid, Ve kurex – x² +6.58² -54-2 da. V = 1.28316 Codice units Vertical distance, he towy - gen) = (x²2x _x² +6.5x2-547) che m (1-2) - GR + 134-5 la CECY (262)-2) -44*+361945 - - 3.847

Cross Sections are Senancircle. Radius of Correction = goog-fen) re (x445x - 65x² +1+0 ) Aren och of de A element A = R Coo T (x +5x6.5x² + 1 teren) Volume of element I = Ada Total volume of solid VE SAda Sta (24+5x + 6.5x tite x 2) 2 de 26 V = f (41876) V = 102564 T Cusic with