题目
设S为曲面z=2-x^2-y^2(zgeq0)，D为x^2+y^2leq2，则积分iint_S dS=().A. int_(0)^2pi dtheta int_(0)^sqrt(2) sqrt(1+4r^2) r drB. int_(0)^2pi dtheta int_(0)^1 sqrt(1+4r^2) r drC. iint_(D) sqrt(4x^2+4y^2) dx dyD. int_(0)^2pi dtheta int_(0)^2 sqrt(1+4r^2) r dr
设$S$为曲面$z=2-x^2-y^2$($z\geq0$)，$D$为$x^2+y^2\leq2$，则积分$\iint_S dS=$().
A. $\int_{0}^{2\pi} d\theta \int_{0}^{\sqrt{2}} \sqrt{1+4r^2} r dr$
B. $\int_{0}^{2\pi} d\theta \int_{0}^{1} \sqrt{1+4r^2} r dr$
C. $\iint_{D} \sqrt{4x^2+4y^2} dx dy$
D. $\int_{0}^{2\pi} d\theta \int_{0}^{2} \sqrt{1+4r^2} r dr$
题目解答
答案
A. $\int_{0}^{2\pi} d\theta \int_{0}^{\sqrt{2}} \sqrt{1+4r^2} r dr$