If the Infinite Curve $y = e ^ { x } , x \geq 0$

question 92

Multiple Choice

If the infinite curve $y = e ^ { x } , x \geq 0$ , is rotated about the $x$ -axis, find the area of the resulting surface. Select the correct answer.

• A) \(\pi [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)
• B) \(\frac { \pi } { 3 } [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)
• C) \(\frac { \pi } { 6 } [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)
• D) \(\frac { \pi } { 6 } [ \sqrt { 3 } + \ln ( 1 + \sqrt { 3 } ) ]\)
• E) \(\frac { \pi } { 4 } [ \sqrt { 2 } + \ln ( 1 + \sqrt { 2 } ) ]\)

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Definitions:

Above Face Value

A term used when a security is traded at a price higher than its nominal or face value.

Accrued Interest

Interest that has been incurred but not yet paid.

Interest Method

A technique used in finance to calculate the interest portion of a loan or investment payment, often employed in amortizing a bond discount or premium.

Effective Interest Method

A method of calculating the amortized cost of a bond and the amount of interest expense over the life of the bond by applying the effective interest rate to the carrying amount of the bond.