AutoSave OFF A A PCGP ... MTH_1009_final_G_23s (OL) [77] - Read-Only - Compatibility Mode - Saved to my Mac iCloud Storage is Full Home Insert Draw Design Layout References Mailings Review View ? Tell me Upgrade your storage to keep using iCloud. " A A Aa Ap ab A A AaBbCcDdE AaBbCcD AaBbCcDdE AaBbCcDdl AaBbCcDdEe Paste BIUvab X X|ADVA A Emphasis Heading 1 Norma Strong Subtitle Styles Dictate Editor Pane 1 5. (See the file 20C_Integral_calculus_stud.doc and problem #5 in the file 24C_pre_final_problems_MTH_1009_20f_sol.doc.) Use the integral calculus methods to evaluate the area bounded by the red graph of g(x) = 2N2 - x2 and blue graph of f(x) = x2 (for any value of N they look similarly to the graphs shown in Fig. 3 for N=1). Fig. 3 (for N = 1) Functions f(x) (blue) and g(x) (red) 2.5 1.5 f(x), g(x) 0.5 -2 1/5 - 1 -0.5 0/5 15 -0.5 Solution (the fist steps). Let us designate the x-coordinates of the left and right points of intersection of two graphs as x1 and x2, respectively. The asked-for area A can be found as a difference of two areas. The first one is the area A, between the red graph of g(x) = 2N2 - x2 and the symmetric interval [x1, X2] on the x-axis. The second one is the area A2 between the blue graph of f(x) = x2 and the interval [X1, X2] on the x-axis. Each area Al and A2 can be presented as a corresponding definite integral: Al = J g(x)dx x2 A2 = Jf(x) dx In order to evaluate these integrals we'd first solve the algebraic equation f(x) = g(x) to determine the x-coordinates x1 and x2 of the points of intersection of the graphs of two Page 7 of 10 1371 words French (France) Focus + 138%