/? x f(x，y)]=？ /? x [3-(x^2+y^2)]=-2x

/? y f(x，y)]=？ /? y [3-(x^2+y^2)]=-2y

Area=A=∫∫ (on 0 ≤ x 2+y 2 ≤ 2) {1+[? /? x [？ (x，y)]]？ + [? /? y [？ (x，y)]]？ } }^( 1/2) dxdy

= ∫∫ (in 0 ≤ x 2+y 2 ≤ 2) {1+4 (x 2+y 2)} dxdy

In polar coordinates,

X=r*cos(a)

Y=r*sin(a)

A=∫∫ (about 0 ≤ R 2 ≤ 2, 0 ≤ A ≤ 2π) {(1+4 (r 2) [cos (a)] 2+[sin (a)] 2} (/kloc-)

= ∫ ∫ (For 0 ≤ r 2 ≤ 2, 0 ≤ a ≤ 2 π) {(1+4 (r 2)} (1/2) Dr. R.

= 2π ∫ (0 ≤ r 2 ≤ 2) {(1+4 (r 2)} (1/2) r dr

= 2π[(2/3){(r/4){2r√( 1 + 4r？ )+ ln|2r + √( 1 + 4r？ )|} + (? ){rln|2r+ √( 1 + 4r？ )| - √( 1 + 4r？ )}}] _ Calculate r from 0 to 2

= 2π[(2/3){( 1/2){ 4 √( 1 7)+ln | 4+√( 17)| }+(？ ){ 2ln | 4+√( 17)|-√( 17)} }]+π/2