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