A thin wire in the shape of a quarter-circle $\mathbf { r } ( t ) = 6 \cos t \mathbf { i } + 6 \sin t \mathbf { j } , 0 \leq t \leq \frac { \pi } { 2 }$, has a linear mass density $\pi ( x , y ) = 2 x + 4 y$. Find the mass and the location of the center of mass of the wire.

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The Answer of A thin wire in the shape of a quarter-circle $\mathbf { r } ( t ) = 6 \cos t \mathbf { i } + 6 \sin t \mathbf { j } , 0 \leq t \leq \frac { \pi } { 2 }$, has a linear mass density $\pi ( x , y ) = 2 x + 4 y$. Find the mass and the location of the center of mass of the wire.

A Thin Wire in the Shape of a Quarter-Circle r(t)=6cos⁡ti+6sin⁡tj,0≤t≤π2\mathbf { r } ( t ) = 6 \cos t \mathbf { i } + 6 \sin t \mathbf { j } , 0 \leq t \leq \frac { \pi } { 2 }r(t)=6costi+6sintj,0≤t≤2π​

A Thin Wire in the Shape of a Quarter-Circle $\mathbf { r } ( t ) = 6 \cos t \mathbf { i } + 6 \sin t \mathbf { j } , 0 \leq t \leq \frac { \pi } { 2 }$