人工智能教程 – 数学基础课程1.1 – 数学分析(一)22 24 数值积分三角函数的积分

数值积分 DART BOARD 圆靶 Assumption1 hits=ce−r2hits=ce^{-r^2}hits=ce−r2 r1<r=x<r2r_1<r=x<r_2r1​<r=x<r2​ Shells: Part=∫r1r2(2πr)e−r2drPart = \int_{r_1}^{r_2}(2 \pi r)e^{-r^2}drPart=∫r1​r2​​(2πr)e−r2dr =−πe−r2∣r1r2=- \pi e^{-r^2}|_{r_1}^{r_2}=−πe−r2∣r1​r2​​ =π(e−r12−e−r22)=\pi (e^{-r_1^2}-