Find the Arc Length of the Curve on the Given $$x = \sqrt { t } , y = 3 t - 2,0 \leq t \leq 3$$

question 119

Multiple Choice

Find the arc length of the curve on the given interval. $$x = \sqrt { t } , y = 3 t - 2,0 \leq t \leq 3$$

• A) \(\frac { \ln ( 864 + 24 \sqrt { 327 } ) + \ln 2 + 12 \sqrt { 327 } } { 24 }\)
• B) \(\frac { \ln ( 864 + 12 \sqrt { 327 } ) - \ln 2 + 6 \sqrt { 327 } } { 24 }\)
• C) \(\frac { \ln ( 864 + 12 \sqrt { 327 } ) + \ln 2 + 12 \sqrt { 165 } } { 48 }\)
• D) \(\frac { \ln ( 864 + 12 \sqrt { 327 } ) + \ln 2 + 12 \sqrt { 165 } } { 24 }\)
• E) \(\frac { \ln ( 864 + 24 \sqrt { 327 } ) - \ln 2 + 12 \sqrt { 327 } } { 24 }\)

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Definitions:

Hypothetical Syllogism

A form of logical argument where two conditional statements lead to a conclusion if the first condition is true, then the conclusion follows.

Modus Ponens

A form of logical argument that concludes a certain consequent from a single premise in the form "If P, then Q" and P, therefore Q.

Modus Tollens

A form of deductive argument in logic that, if the implication is true, then denies the consequent to conclude the denial of the antecedent.

Proposition

A declarative sentence that can be evaluated as true or false, conveying a statement or assertion.