Find the Length of the Curve $\mathrm { r } = \mathrm { e } ^ { 2 \theta } , 0 \leq \theta \leq \pi$

question 2

Multiple Choice

Find the length of the curve.
-The spiral $\mathrm { r } = \mathrm { e } ^ { 2 \theta } , 0 \leq \theta \leq \pi$

• A) \(\frac { 1 } { 8 } \left( e ^ { 4 \pi } - 1 \right)\)
• B) \(\frac { \sqrt { 5 } } { 2 } \left( e ^ { 2 \pi } - 1 \right)\)
• C) \(e ^ { 4 \pi } - \sqrt { 3 }\)
• D) \(\frac { 16 } { 3 } \left( \pi ^ { 2 } - 1 \right)\)

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Definitions:

Induced Labor

The medical process of artificially initiating childbirth, often through the use of medications or other methods, before natural labor begins on its own.

C-section Births

Childbirth through a surgical procedure called a cesarean section, where the baby is delivered through an incision in the mother's abdomen and uterus.

Vaginal Births

The natural process of delivering a baby through the birth canal.

Home Births

The practice of giving birth in a non-clinical, home setting, often assisted by a midwife or doula.