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用WolframAlpha求平面图形的面积

2011-08-31 21:35:13| 分类： WolframAlpha | 标签： |举报 |字号大中小订阅

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先作图输入：plot x^3-2x from x=-2 to 2

网址： http://www.wolframalpha.com/input/?i=plot+x%5E3-2x+from+x%3D-2+to+2

解方程求曲线与x轴的交点。输入： solve x^3-2x

http://www.wolframalpha.com/input/?i=solve+x%5E3-2x

求面积： A=int abs( x^3-2x) from -sqrt(2) to sqrt(2)

http://www.wolframalpha.com/input/?i=A%3Dint+abs%28+x%5E3-2x%29+from+-sqrt%282%29+to+sqrt%282%29

另解直接求面积

输入： area between x^3-2x and the x-axis

http://www.wolframalpha.com/input/?i=area+between+x%5E3-2x+and+the+x-axis

结果有误！

两曲线之间的面积

先作图：plot x^2, x^3

http://www.wolframalpha.com/input/?i=plot+x%5E2%2C+x%5E3

求交点：solve x^2=x^3

http://www.wolframalpha.com/input/?i=solve+x%5E2%3Dx%5E3

求面积： A=int x^2-x^3 from 0 to 1

http://www.wolframalpha.com/input/?i=A%3Dint+x%5E2-x%5E3+from+0+to+1

用WolframAlpha求平面图形的面积 - calculus - 高等数学

另解直接求两曲线之间的面积

输入： area between x^2 and x^3

http://www.wolframalpha.com/input/?i=area+between+x%5E2+and+x%5E3

很方便！

先作图： plot sin(x), cos(2x) from 0 to pi

http://www.wolframalpha.com/input/?i=plot+sin%28x%29%2C+cos%282x%29+from+0+to+pi

求面积：integrate abs(sin(x)-cos(2x)) from x=0 to pi

http://www.wolframalpha.com/input/?i=integrate+abs%28sin%28x%29-cos%282x%29%29+from+x%3D0+to+pi

另解：直接求面积

输入： area between sin(x) and cos(2x) from x=0 to pi

http://www.wolframalpha.com/input/?i=area+between+sin%28x%29+and+cos%282x%29+from+x%3D0+to+pi

很方便！

再补充一个例子

先作图：plot 2-x^2>e^x, x=-2..2< xmlnamespace prefix ="o" ns ="urn:schemas-microsoft-com:office:office" />

http://www.wolframalpha.com/input/?i=plot+2-x%5E2%3Ee%5Ex%2C+x%3D-2..2

求交点： solve 2-x^2=e^x

http://www.wolframalpha.com/input/?i=+solve+2-x%5E2%3De%5Ex

求面积：int 2-x^2-e^x, x=-1.31597..0.537274

http://www.wolframalpha.com/input/?i=int+2-x%5E2-e%5Ex%2C+x%3D-1.31597..0.537274

最后介绍一种简便方法。

用Boole函数比较方便。不必求交点

输入： integrate (2-x^2-e^x)Boole(2-x^2>e^x), x=-oo..oo

网址：http://www.wolframalpha.com/input/?i=integrate+%282-x%5E2-e%5Ex%29Boole%282-x%5E2%3Ee%5Ex%29%2C+x%3D-oo..oo

返回《用WolframAlpha做微积分》总目录：

http://xuxzmail.blog.163.com/blog/static/251319162011730102030274/

用WolframAlpha求平面图形的面积 - calculus - 高等数学

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