Find the area of the surface. The part of the paraboloid $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k }$ ; $0 \leq u \leq 7$ , $0 \leq v \leq 2 \pi$
A) $\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 12 }$
B) $\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 3 }$
C) $\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 6 }$
D) $\frac { 5 \pi ( 197 \sqrt { 197 } - 1 ) } { 12 }$

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The Answer of Find the area of the surface. The part of the paraboloid $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k }$ ; $0 \leq u \leq 7$ , $0 \leq v \leq 2 \pi$
A) $\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 12 }$
B) $\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 3 }$
C) $\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 6 }$
D) $\frac { 5 \pi ( 197 \sqrt { 197 } - 1 ) } { 12 }$

Find the Area of the Surface r(u,v)=ucos⁡vi+usin⁡vj+u2k\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k }r(u,v)=ucosvi+usinvj+u2k

Find the Area of the Surface $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k }$