Sufrace Area Continued!!

Calculus Level 5

Consider the graph of the curve $y=\sin(x)$ on the interval from $x=0$ to $x=\pi$ .

What is the surface area formed by its revolution around the $x$ -axis to $4$ decimal places?

The answer is 14.4235.

1 solution

Kunal Gupta
Feb 16, 2015

Using the formula for Surface Area, we get: $Area =\displaystyle\int _{ 0 }^{ \pi }{ 2\pi \sin { x } \sqrt { 1+{ (\cos { x } ) }^{ 2 } } dx }$ which equals: $2\sqrt{2}\pi + \pi \log { \left[ \frac { \sqrt { 2 } +1 }{ \sqrt { 2 } -1 } \right] } \approx 14.4240$

Sufrace Area Continued!!

The answer is 14.4235.

1 solution

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