The Laplace Transform Of $\int _ { 0 } ^ { t } e ^ { \tau } \sin ( t - \tau ) d \tau$

question 8

Multiple Choice

The Laplace transform of $\int _ { 0 } ^ { t } e ^ { \tau } \sin ( t - \tau ) d \tau$ is

• A) \(1 / \left( ( s - 1 ) \left( s ^ { 2 } + 1 \right) \right)\)
• B) \(1 / \left( ( s + 1 ) \left( s ^ { 2 } + 1 \right) \right)\)
• C) \(s / \left( ( s - 1 ) \left( s ^ { 2 } + 1 \right) \right)\)
• D) \(s / \left( ( s + 1 ) \left( s ^ { 2 } + 1 \right) \right)\)
• E) \(1 / \left( ( s - 1 ) \left( s ^ { 2 } - 1 \right) \right)\)

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Definitions:

Average Total Cost

The total cost of production divided by the quantity of output produced.

Total Cost

The complete cost of production, including both fixed and variable costs, incurred by a firm in producing and selling a certain amount of a good or service.

Fixed Costs

Expenses that remain constant regardless of the level of outputs, like lease payments or property taxes.

Marginal Costs

The upsurge in complete costs linked to the production of a supplementary unit of a good or service.