基础高数二重积分1.∫∫D(x²-y²)dxdy ,0
问题描述:
基础高数二重积分
1.∫∫D(x²-y²)dxdy ,0
答
1.∫∫D(x²-y²)dxdy =∫(0,π)dx∫(0,sinx)(x²-y²)dy =∫(0,π)dx[x²sinx - (sin³x)/3]=∫(0,π)[x²(-dcosx) + (sin²x)(dcosx)/3]=∫(0,π)[(1-cos²x)(dcosx)/3] - ...