= 2 a | \cos \theta $$ 2|dθ∴心形线的全长为:$$ s = 2 a \int 2 \pi 0 | \cos \theta $$ 2 $$ 2 | d \theta = 2 a \int \pi 0 \cos \theta 2 d \theta + 2 a \int 2 \pi \pi ( ? \cos $$ $$ \theta 2 ) d \theta = 4 a \sin \theta 2 | \pi 0 ?
【解析】 解 由对称性知$$ \overline { y } = 0 $$.注意到 $$ d s = \sqrt { r ^ { 2 } ( \theta ) + [ r ^ { \prime } ( \theta ) ] ^ { 2 } } d \theta - \sqrt { 2 } a \sqrt { 1 - \cos \theta } d \theta $$ $$ \overline { x } = \frac {...