Find the Area of the Region Bounded By $x = e ^ { t } \cos t , y = e ^ { t } \sin t , 0 \leq t \leq \pi$

question 177

Multiple Choice

Find the area of the region bounded by $x = e ^ { t } \cos t , y = e ^ { t } \sin t , 0 \leq t \leq \pi$ , and the x-axis.

• A) \(\frac { 1 } { 4 } e ^ { 2 x }\)
• B) \(\frac { 1 } { 2 } e ^ { 2 x }\)
• C) \(\frac { 1 } { 4 } \left( e ^ { 2 x } + 1 \right)\)
• D) \(\frac { 1 } { 4 } e ^ { x }\)
• E) \(\frac { 1 } { 4 } \left( e ^ { 2 x } - 1 \right)\)
• F) \(\frac { 1 } { 2 } \left( e ^ { 2 x } - 1 \right)\)
• G) \(\frac { 1 } { 2 } \left( e ^ { x } - 1 \right)\)
• H) \(e ^ { 2 x } - 1\)