微积分.Acurveissuchthatdy/dx=16/x^3,and(1,4)isapointonthecurve.(i)Findtheequationofthecurve.(ii)Alinewithgradient-1/2isanormaltothecurve.Findtheequationofthiscurve,givingyouranswerintheformax+by=c(iii)Findt
1人问答
问题描述：
微积分.
Acurveissuchthatdy/dx=16/x^3,and(1,4)isapointonthecurve.
(i)Findtheequationofthecurve.
(ii)Alinewithgradient-1/2isanormaltothecurve.Findtheequationofthiscurve,givingyouranswerintheformax+by=c
(iii)Findtheareaoftheregionenclosedbythecurve,thex-axisandthelinesx=1andx=2
唐明军回答：
这题得用积分.
这个函数的微分是16/x^3=16x-3.theintergralofthederivativeoftheoriginalfunctionshouldbetheoriginalfunctionwhichistheequationofthecurve.Thus∫16/x^3dx=-8/x^2+cthenwetake(1,4)intotheequationandsolveforc.theresultisc=12.Sotheequationofthecurveis-8/x^2+12.
thelineisnormaltothecurvemeansitssloapisreciprocaltothesloapofthecurve.iamsureyoucandealwiththerestofit.
∫from1to2of16/x^3dx=-6
theareaisthus6
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