What is the area of the blue shaded region
1 answer:
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(a) You can parameterize <em>C</em> by the vector function
<em>r</em><em>(t)</em> = (<em>x(t)</em>, <em>y(t)</em> ) = <em>P</em> (1 - <em>t </em>) + <em>Q</em> <em>t</em> = (2 - 2<em>t</em>, 7<em>t</em> )
where 0 ≤ <em>t</em> ≤ 1.
(b) From the above parameterization, we have
<em>r</em><em>'(t)</em> = (-2, 7) ==> ||<em>r</em><em>'(t)</em>|| = √((-2)² + 7²) = √53
Then
d<em>s</em> = √53 d<em>t</em>
and the line integral is
(c) The remaining integral is pretty simple,