# OEF 几何积分 --- 介绍 ---

### 显式方程的弧长 2D

xrange , yrange , arrow ,0,,0,10,grey arrow 0,,0,,10,grey plot skyblue, trange , linewidth 3 plot blue,

### 参数方程的弧长 2D

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xrange , yrange , trange , arrow ,0,,0,10,grey arrow 0,,0,,10,grey plot skyblue,, trange , linewidth 3 plot blue,,

### 闭的极坐标长度

xrange -, yrange -, fill 0,0,white tstep 500 trange , arrow 0,0,,0,12,grey disk 0,0,6,red plot skyblue,()*cos(t),()*sin(t) trange , linewidth 2 plot blue,()*cos(t),()*sin(t)

### 开的极坐标长度

xrange -, yrange -, fill 0,0,white tstep 500 trange , arrow 0,0,,0,12,grey disk 0,0,6,red plot skyblue,()*cos(t),()*sin(t) trange , linewidth 2 plot blue,()*cos(t),()*sin(t)

### 螺线极坐标长度

xrange -, yrange -, fill 0,0,white tstep 500 trange , arrow 0,0,,0,12,grey disk 0,0,6,red plot skyblue,()*cos(t),()*sin(t) trange , linewidth 2 plot blue,()*cos(t),()*sin(t)

### 已知对数面积

xrange , yrange , arrow ,0,,0,10,grey arrow 0,,0,,10,grey text grey,0.95*,0.1*,small,x text grey,0.03*,0.98*,small,y trange 0, plot black,t, vline ,0,red fill 0.8*,0.2*,skyblue

### 已知二次面积 *

xrange , yrange , plot black, arrow ,0,,0,10,grey fill ,*(-1)*0.1,yellow arrow 0,,0,,10,grey text grey,-0.04*,0.07*,small,x text grey,0.03*,-0.01*,small,y

### 旋转体面积

xrange , yrange , arrow ,0,,0,10,grey arrow 0,,0,,10,grey text black,-0.04*(),0.08*(),small,x text black,0.03*(),-0.02*(),small,y dline ,0,,,black dline ,0,,,black trange , plot red, v=0.3 u=0.8 r=-0.12*() m=0.03* n=0.07* trange v,2*pi-v plot black,m*cos(t)+r,n*sin(t) arrow m*cos(u)+r,n*sin(u),m*cos(v)+r,n*sin(v),8,black

### 旋转体体积

xrange , yrange , arrow ,0,,0,10,grey arrow 0,,0,,10,grey text black,-0.04*(),0.08*(),small,x text black,0.03*(),-0.02*(),small,y dline ,0,,,black dline ,0,,,black trange , plot red, v=0.3 u=0.8 r=-0.12*() m=0.03* n=0.07* trange v,2*pi-v plot black,m*cos(t)+r,n*sin(t) arrow m*cos(u)+r,n*sin(u),m*cos(v)+r,n*sin(v),8,black

The most recent version

• Description: 一组关于单变量函数积分几何应用的练习. interactive exercises, online calculators and plotters, mathematical recreation and games
• Keywords: interactive mathematics, interactive math, server side interactivity, analysis, integral, definite integral, area, volume