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) \(1 / \left( ( s - 1 ) \left( s ^ { 2 } - 1 \right) \right)\)

---

Definitions:

Dependent

In various contexts, it refers to something that relies on or is determined by another factor, such as a variable in programming or mathematics.

Replace

A feature in software applications that allows the user to search for and replace specific text, numbers, or formats within a document.

Function

In computing and programming, a sequence of code executed to perform a specific task and often returns a value.

Formula

A formula is an expression entered into a spreadsheet cell to calculate a value based on the data in other cells.