旋转体体积：垫圈法
2015-04-21 05:01
本范例演示了如何使用垫圈法计算中空旋转体的体积。通过积分公式 π∫[a,b]([f(x)]²-[g(x)]²)dx，直观展示了由两条曲线 f(x) 和 g(x) 绕轴旋转所形成的立体图形。用户可以调整函数和积分区间，观察垫圈的生成过程及体积的累积，深入理解定积分在立体几何中的应用。
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<element type="text" label="txtShowDisks">
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<element type="point3d" label="P4">
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<element type="text" label="txtIntegral">
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<element type="segment" label="segA">
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<element type="segment" label="segB">
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<expression label="text1" exp=""f(x)=" + (LaTeX[f]) + """ />
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<output a0="gCurveT1"/>
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<element type="conicpart" label="thetaArc">
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<command name="CurveCartesian">
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<element type="curvecartesian3d" label="gCurveT2">
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<command name="Surface">
<input a0="t" a1="(g(t) * cos(s))" a2="(g(t) * sin(s))" a3="t" a4="a" a5="b" a6="s" a7="θ1" a8="θ2"/>
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<element type="surfacecartesian3d" label="surfaceG">
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<condition showObject="showWashers"/>
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<output a0="ringsL"/>
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<expression label="f2" exp="f2(x) = If[x1 ≤ x ≤ x2,f]" />
<element type="function" label="f2">
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<element type="textfield" label="inputBox2">
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<linkedGeo exp="g"/>
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