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. iint_(D)sqrt(4x^2+4y^2) , dx , dyB. int_(0)^2pi dtheta int_(0)^1 sqrt(1+4r^2) , r , drC. int_(0)^2pi dtheta int_(0)^sqrt(2) sqrt(1+4r^2) , r , drD. 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. $\iint_{D}\sqrt{4x^2+4y^2} \, dx \, dy$
B. $\int_{0}^{2\pi} d\theta \int_{0}^{1} \sqrt{1+4r^2} \, r \, dr$
C. $\int_{0}^{2\pi} d\theta \int_{0}^{\sqrt{2}} \sqrt{1+4r^2} \, r \, dr$
D. $\int_{0}^{2\pi} d\theta \int_{0}^{2} \sqrt{1+4r^2} \, r \, dr$
题目解答
答案
C. $\int_{0}^{2\pi} d\theta \int_{0}^{\sqrt{2}} \sqrt{1+4r^2} \, r \, dr$