逐步演示壳层法求旋转体体积

GeoGebra 命令及参数

1. LaTeX(("\text{step }" * steps)) → text1
2. LaTeX("\text{The general form of the integrand is } 2\pi(radius)(height)\text{.}") → text3
3. Point(xAxis) → A
4. Segment((x(A), g(x(A))), (x(A), f(x(A)))) → h
5. Point(h) → B
6. Segment(B, (2, y(B))) → r
7. LaTeX("\text{In this case the radius is given by }\textcolor{#FF33CC}{r}=x-\textcolor{#CC0000}{2}\text{.}") → text4
8. LaTeX("\text{The integration limits come from the x-coordinates of the}\cr\text{intersection points of functions }\textcolor{#000099}{f}\text{ and }\textcolor{#339900}{g}.") → text6
9. LaTeX((((((("\text{Use cylindrical shells to calculate the volume swept out when the}\cr\text{region enclosed by the functions }\textcolor{#0033CC}{f=" * f) * "}\text{ and }\textcolor{#339900}{g=e^{") * a) * "x}}\text{ is}\cr\text{revolved around the line }\textcolor{#CC0000}{") * c) * "}.")) → text2
10. LaTeX("\text{The height }\textcolor{#FF6600}{h}\text{ is given by }\textcolor{#0033CC}{f(x)}-\textcolor{#339900}{g(x)}.") → text5
11. LaTeX((((((((("V=2\pi\int_{" * Lintersect) * "}^{") * Rintersect) * "}(x-2)\left[(") * f) * ")-(") * g) * ")\right]dx")) → text7
12. Mirror(fcut, c) → fshadow
13. Mirror(gcut, c) → gshadow
14. Mirror(h, c) → h'
15. Mirror(r, c) → r'