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

question 80

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) \(\frac { \ln ( 864 + 24 \sqrt { 327 } ) - \ln 2 + 12 \sqrt { 327 } } { 24 }\)

---

Definitions:

Antipyretics

Medications or substances used to reduce fever, such as acetaminophen or ibuprofen.

Hypothalamus

A structure of the brain between the cerebrum and the midbrain; lies below the thalamus.

Laxative

A substance that induces the bowels to empty.

Antidiarrheal

A medication or substance used to prevent or alleviate symptoms of diarrhea.