Question 1074558
Find the points of intersection, you can read it off the graph or solve.
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*[illustration f13.JPG].
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{{{10sin(theta)=5}}}
{{{sin(theta)=1/2}}}
{{{theta=30}}} and {{{theta=150}}}
So then,
{{{A=int((1/2)((10sin(theta))^2-5^2),d(theta),30,150)}}}
{{{A=25x-50sin(x)cos(x)+C}}}
Convert the angles to radians,
{{{30*((2pi)/360)=pi/6}}}
{{{150*((2pi)/360)=(5/6)pi}}}
So,
{{{2A=25pi(5/6-1/6)-50(sin((5/6)pi)cos((5/6)pi)-sin(pi/6)cos(pi/6))}}}
{{{2A=25pi(4/6)+43.30127}}}
{{{2A=52.35988+43.30127}}}
{{{2A=95.66}}}
So,
{{{A=47.83}}}