求解一道大一高数题,如图
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 01:07:16
![求解一道大一高数题,如图](/uploads/image/z/1824350-14-0.jpg?t=%E6%B1%82%E8%A7%A3%E4%B8%80%E9%81%93%E5%A4%A7%E4%B8%80%E9%AB%98%E6%95%B0%E9%A2%98%2C%E5%A6%82%E5%9B%BE)
求解一道大一高数题,如图
求解一道大一高数题,如图
求解一道大一高数题,如图
转换到极坐标系,则x²+y²=r²,dxdy=rdrdθ,积分域为r∈[0,+∞),θ∈[π/4,π/3]
∫(0,+∞)dx∫(x,√3x) e^[-(x²+y²)] dy
=∫(0,+∞)rdr∫(π/4,π/3) e^(-r²) dθ
=∫(0,+∞)re^(-r²)dr*(π/3-π/4)
=(π/6)*(1/2)∫(0,+∞)e^(-r²)dr²
=-(π/12)*e^(-r²)|(0,+∞)
=-(π/12)*(0-1)
=π/12