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img005hs6 - 6 Chapter 6 Applications of Integration ——...

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Unformatted text preview: 6 Chapter 6 Applications of Integration ——_ 29. The points of intersection are given by: 30. The points of intersection are given by: 33+ —4x+3=3+4x—x= .r‘—21t’=2x3 Mir-4H0 when x=0.4 x:(,2-4)=0 when x=0.:l:2 4 1 =f [(3+4x—x1)—tx=—4x+a)]dx A=2IE2x!—(x4—2x1)]dx o D 4 1 =I (—2x‘+8x)dx =21)“: —r‘)dx I 0 2:3 4 64 _[_ 3 +4R]o_ 3 Numerical Approximation: 21.333 [4:3 .I’z_128 31. fix) = x‘ — 4x3. g(x) = x2 - 4 . _‘-fll'. The points of intersecu'on am given by: x‘-— 4,221.: — x‘ — 512 + 4 = 0 {x3 - 4){X:- 1) =0 when x=:l:2.:i:l By symmetry. 1 A=2L[{x‘~4x‘)-(x1—4)]¢£t+2'[ [(x1—4J—w—4x1ndx =2£Ix‘—5x‘+4)dx+2f(—x‘+5x2-4)dx x5 5:3 =2[———+4x]; +2[—-—+—-4x]: -2[;-;+41+2[(-—+%—s>- (-%+%-4)]=& Numerical Approximation: 5.067 + 2.933 = 8.0 32. fix) = x‘ — 4x2. 3(1) = x3 - 4x The points of intersection are given by: x‘- 4x3= :3 — 4.1: x‘ — x3 — 4x1 + 4x = 0 .10: - ”(x + 2)(x — 2) = 0 when x = —2.IJ.],2 = f" [w — 4x) — w — 41mm + f [(x‘ - 4x2)— (x3 — mm + [m3 — 4.; — w — 4.2)de ‘1 D 248 53 293 =__._+3_.+_..=_ 30 60 60 30 Numerical Approximation: 8.267 + 0.61? + 0.883 ~ 9.767 ...
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