设 $D=\{(x,y)|x^2+y^2\le 4, y\ge 0\}$,则二重积分 $\iint_D xy^2dxdy=$______ .
举一反三
- 设\(D\)是由直线\(y = x,y = x + 1,y = 1\)及\(y=3\)所围成的区域,则二重积分\(\iint\limits_D {({x^2} + {y^2} - y)dxdy = }\)______
- 设\(D\)是由直线\(y=x,y=x+a,y=a\)及\(y=3a(a>0)\)所围成的区域,则二重积分\(\iint\limits_D {({x^2} + {y^2})dxdy =}\)( )。 A: \(14{a^4}\) B: \(14{a^3}\) C: \(12{a^3}\) D: \(12{a^4}\)
- 设D是由\( {x^2} + {y^2} \le 1 \) ,\( x \ge 0 \) ,\( y \ge 0 \) 所围区域,则\( \int\!\!\!\int\limits_D {x{y^2}} dxdy \) =( ) A: \( {1 \over 5} \) B: \( {1 \over {15}} \) C: \( {2 \over {15}} \) D: 1
- 设\(D = \left\{ {(x,y)\left| { { x^2} + {y^2} \le 9,x \ge 0,y \ge 0} \right.} \right\}\),则\(\int\!\!\!\int\limits_D {(x + 3y)} d\sigma = \)______
- 设\(D = \left\{ {(x,y)\left| { { x^2} + {y^2} \le 4,x \ge 0,y \ge 0} \right.} \right\}\),则\(\int\!\!\!\int\limits_D {(x + y)} d\sigma = \) A: \(0\) B: \( { { 8} \over 3}\) C: \( { { 16} \over 3}\) D: \( { { 32} \over 3}\)