题目
设Omega为区域x^2+y^2+z^2leq z，则iiint_(Omega)(x^2+y^2+z^2)dxdydz=A. int_(0)^2pidthetaint_(0)^pidvarphiint_(0)^cosvarphir^3sinvarphi drB. int_(0)^2pidthetaint_(0)^(pi)/(2)dvarphiint_(0)^cosvarphir^4sinvarphi drC. int_(0)^2pidthetaint_(0)^(pi)/(2)dvarphiint_(0)^(1)/(2)r^3sinvarphi drD. int_(0)^2pidthetaint_(0)^(pi)/(2)dvarphiint_(0)^1r^3sinvarphi dr
设$\Omega$为区域$x^{2}+y^{2}+z^{2}\leq z$，则$\iiint_{\Omega}(x^{2}+y^{2}+z^{2})dxdydz=$
A. $\int_{0}^{2\pi}d\theta\int_{0}^{\pi}d\varphi\int_{0}^{\cos\varphi}r^{3}\sin\varphi dr$
B. $\int_{0}^{2\pi}d\theta\int_{0}^{\frac{\pi}{2}}d\varphi\int_{0}^{\cos\varphi}r^{4}\sin\varphi dr$
C. $\int_{0}^{2\pi}d\theta\int_{0}^{\frac{\pi}{2}}d\varphi\int_{0}^{\frac{1}{2}}r^{3}\sin\varphi dr$
D. $\int_{0}^{2\pi}d\theta\int_{0}^{\frac{\pi}{2}}d\varphi\int_{0}^{1}r^{3}\sin\varphi dr$
题目解答
答案
B. $\int_{0}^{2\pi}d\theta\int_{0}^{\frac{\pi}{2}}d\varphi\int_{0}^{\cos\varphi}r^{4}\sin\varphi dr$