close
標題:
ddfinite integration
發問:
Show thatthe volume of a sphere with the radius of r is (4/3) πr^3 by definiteintegration. Consider the equation (x^2)+(y^2)=r^2
最佳解答:
V = π ∫ [f(x)]^2 dx By symmetry, we only need to consider the positive value of x From x^2 + y^2 = r^2 y^2 = r^2 - x^2 and the largest value of x is r So, V = 2π ∫ [f(x)]^2 dx [from 0 to r] = 2π ∫ (r^2 - x^2) dx [from 0 to r] = 2π(r^3 - x^3/3 | [0,r]) = 2π(r^3 - r^3/3) = 4πr^3/3
其他解答:
ddfinite integration
發問:
Show thatthe volume of a sphere with the radius of r is (4/3) πr^3 by definiteintegration. Consider the equation (x^2)+(y^2)=r^2
最佳解答:
V = π ∫ [f(x)]^2 dx By symmetry, we only need to consider the positive value of x From x^2 + y^2 = r^2 y^2 = r^2 - x^2 and the largest value of x is r So, V = 2π ∫ [f(x)]^2 dx [from 0 to r] = 2π ∫ (r^2 - x^2) dx [from 0 to r] = 2π(r^3 - x^3/3 | [0,r]) = 2π(r^3 - r^3/3) = 4πr^3/3
其他解答:
此文章來自奇摩知識+如有不便請留言告知
文章標籤
全站熱搜
留言列表
