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Moderate

Surface Area from Rotation

APCALC-LKWHE0

Determine which expression represents the surface area of the solid formed by rotating the graph $y = x^2 + 2$ about the $x$-axis from $x = 0$ to $3$.

A

$2\pi \displaystyle\int _{ 0 }^{ 3 }{ x\sqrt { 1+{ 4 }x^{ 2 } } dx } $

B

$2\pi \displaystyle\int _{ 0 }^{ 3 }{ x\sqrt { 1+{ 2 }x } dx } $

C

$2\pi \displaystyle\int _{ 0 }^{ 3 }{ ( { x }^{ 2 }+2 ) \sqrt { 1+{ 4x }^{ 2 } } dx }$

D

$2\pi \displaystyle\int _{ 0 }^{ 3 }{ x\sqrt { 1+{ 4x }^{ 2 } } dx } $