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单选题
∫L(x2+y2+2x)ds=( ),其中曲线L为x2+y2=R2
A
2πR3/3
B
2πR3
C
4πR3
D
πR3
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参考解析
解析:
由曲线方程L为x2+y2=R2可知曲线关于y轴对称,且函数2x是x的奇函数,故∫L2xds=0。故∫L(x2+y2+2x)ds=∫L(x2+y2)ds=∫LR2ds=R22πR=2πR3。
由曲线方程L为x2+y2=R2可知曲线关于y轴对称,且函数2x是x的奇函数,故∫L2xds=0。故∫L(x2+y2+2x)ds=∫L(x2+y2)ds=∫LR2ds=R22πR=2πR3。
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