ALPHA DIVISION

Question 64

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Question

Marvin starts at the origin, travels to the point

\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)

in a straight line, moves along the curve given by

x(t)=\cos t

and

y(t)=\sin t

for

\frac{\pi}{6}\le t\le\frac{\pi}{4}

, then returns to the origin in a straight line. Help Marvin find the area bounded by his path.

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Question

Marvin starts at the origin, travels to the point

\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)

in a straight line, moves along the curve given by

x(t)=\cos t

and

y(t)=\sin t

for

\frac{\pi}{6}\le t\le\frac{\pi}{4}

, then returns to the origin in a straight line. Help Marvin find the area bounded by his path.