【正文】
hematical analysis, the calculation method of diversity, flexibility, this paper summarizes the general methods of calculating the double integral and special calculation method. Among them, the general calculation methods including double integral for the iterated integral and substitution method, symmetry, parity and double integral and integral method special calculation methods including application functions.Key words: The double integral integral symmetry of subsection integral method 12 。 極坐標(biāo)下的換元法例5 計(jì)算二重積分,其中如圖(5)所示. 解 由于區(qū)域由圓的一部分組成,所以可以用極坐標(biāo)變換來求解.設(shè),則在極坐標(biāo)下,被積函數(shù)為,此題是應(yīng)用極坐標(biāo)換元法求解的. 應(yīng)用函數(shù)的對稱性求二重積分定理4 如果積分區(qū)域關(guān)于軸對稱,被積函數(shù)是關(guān)于的偶函數(shù),是的位于軸右側(cè)的部分,則有 如果積分區(qū)域關(guān)于軸對稱,被積函數(shù)是關(guān)于的偶函數(shù),是的位于軸上側(cè)的部分,則有 證明 由于關(guān)于軸對稱,不妨設(shè)y軸將區(qū)域分為和,則由二重積分對區(qū)域的可