題目 13. (15分)(15\text{分})(15分) I(r)=∬Ωrexp[−(x2+2xy+3y2)] dAI(r)=\iint_{\Omega_r}\exp\left[-(x^2+2xy+3y^2)\right]\,dAI(r)=∬Ωrexp[−(x2+2xy+3y2)]dA where Ωr={(x,y)∣x2+2xy+3y2≤r2}\Omega_r=\{(x,y)\mid x^2+2xy+3y^2\le r^2\}Ωr={(x,y)∣x2+2xy+3y2≤r2}。 (a) Evaluate I(1)I(1)I(1). (10分)(10\text{分})(10分) (b) Find limr→∞I(r)\lim_{r\to\infty}I(r)limr→∞I(r). (5分)(5\text{分})(5分) 解答
