The Area Between Two Curves Homework Clipart

Unformatted text preview: Area of a Re 'on Between Two Curves - Homework For each problem, sketch the region bounded by the graphs of the functions and find the region of the area. /’\/-\ 2 y= x 2—4x+3, y=x 1.y=x +2x+1,y=2x+5 2. 3. y=—-x 2+2x+3' y=x Integral-g 9 if? E” [1X r”Mlntegralos'W [XZ’IBI '2 Lfi-q‘xrfid nt:gral:M Z: X3 Area: Area: ______._____________ 1 IE. 4.y=(x—1)3,y=x—1 5.y=%,y=0,x=l,x=5 6. y=\/§+1,y=x,x=0 ‘ §H§ 5)?” W95 Integral: 2 ‘ AX. \ Airfrall 2 X Area: ' . 7. y = V1); = x Integral: Integral: Area: Area: M arterM af/JM enior. com — l 69 — Stu Schwartz 10 y =25111an7 =tanx 1 12 y = x3 and the tangent I —-7£sxs—3E 3 3 Osxsst 'linetoy at (1,1) I y = 25inx,y = cos2x Integral: Integral: Integral: Area: Area: Area: 13. Find the value(s) of b if the vertieal line 1: = b divides the region between x = y =16 - 2x and the x and y— into 2 equal areas. axis 14. Use integration to to find the area of the triangle having the vertices (3, ~2), (5, 7), and (7, 2). 15. Show that the area under the function . 1 3’ = “2 [*afl] IS 3 of the area of the circumscribed rectangle. M arferM :2th enfor. mm —170- Stu Scbwartz ,A. Area of a Re ion Between Two Curves - Homework For each problem, sketch the region bounded by the graphs of the functions and find the region of the area. 2' y=x2 ——4x+3, 1. y=xz+2x+l,y=2x+5 3. y y x2 y=——12+2x+3 x3 j[2x+5—(x2+21+1)]dx j[—xz+2x+3-(x2—4x+3)] air -2 0 Area:10.667 Area: 9 4. y=(X—1)3,y=x——1 5. y=%,y=0,x=1,x=5 6. y=\/§+l,y=x,x=0 5 4,791 fr—12—1dr f[\/§+1—x]d 1 [I J 0 Area:0.8 Area:5.423 1 1 9. = =—x2 y 1+f’y 2 Area:1.237 AB Solutions — 169 — y=2s1nx,y=tanx y=25inx,y=0052x y=x§ and the tangent 10. 11. 12 x~ ”gsxsg— OSXSDT, toyat(1,1) m/3 .375 2.767 1 2f[sinx-tanx] air 2f[cost—23inx] dx+ f[2$inx—cos2x]dx f[x3 —(3x—2)]air o 0 375 _2 Area: 0.614 Area:4.807 Area: 6.750 13. Find the value(s) of b if the vertical line I = b divides the region between )2 =16 — 2xand the x and j—axis into 2 equal areas. f(16~2x)¢r=j(l6—2x)air 0 b 165— 52 =128— 64—(165— 52) 0=2z§2 425+ 64 0= 52 —16b+ 32=> 5:2.343 fl .\ 14. Use integration to to find the area of the triangle having the vertices (3, —2), (5, 7), and (7, 2) 15. Show that the area under the function y: a)? is % ofthe area ofthe circumscribed rectangle. A= 2f (”My Am, = 2443) = 2a4 0 AB Solutions — 170 — ...
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