Sketch and shade the finite region bounded by the curve $y={{x}^{2}}+2$, the lines $y=x$ and \(x

Question

Sketch and shade the finite region bounded by the curve $y={{x}^{2}}+2$, the lines $y=x$ and $x=1$, and the $y$-axis. Find the exact volume of the solid formed when the region is rotated $2\pi $ radians about the $y$-axis.

Accepted Answer

${\frac{11}{6}\pi}$

2014 TJC Promo Q6 (b)

2014 TJC Promo Q6 (b)

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