ddfinite integration
2011-03-21 2:55 am
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
回答 (1)
2011-03-21 3:50 am
✔ 最佳答案
V = π ∫ [f(x)]^2 dxBy 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
收錄日期: 2021-04-20 00:16:11
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