簡單生活 發問時間: 科學數學 · 1 0 年前

高微問題(change of variable)

求這題高微要怎麼解阿

可以給我一個開頭或中間步驟都行

因為沒有想法該從哪裡下手~~

find the mass of a ball of radius R if the mass density is c times the distance

from the boundary of the ball

已更新項目:

恩...感覺好複雜喔>"<

沒有辦法用式子列出來嗎??

1 個解答

評分
  • 1 0 年前
    最佳解答

    Without loss of generality, the ball is centered at the origin : B={(x,y,z)|x^2+y^2+z^2=R^2} = {(rho, theta, phi)|0<rho<R, 0<theta<2pi, 0<phi<pi}.

    the distance from the boundary of the ball =R-rho, if the latter (sherical coordinates) is used.

    Thus the mass of a ball , M=c* triple integral[over B] of {R-rho} dV. To finish the calculation, recognize dV=(rho)^2*sin(phi)*d(rho)d(theta)d(phi) and change the triple integral into iterated integral with the order d(rho) the last will do.

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