Richard P. answered 10/21/16
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for 0 < θ < π/2 , these curves cross at θ =arctan( 31/2 ) = π/3
The cosine curve is the upper one, so the desired area is
A = integral from 0 to π/3 of [ 31/2 cos(θ) - sin(θ) ]
The anti-derivative of the expression in the square brackets is
[ 31/2 sin(θ) + cos(θ) ]
So A = (31/2 sin(π/3) +cos(π/3) ) - (31/2 sin(0) + cos(0) )
Remembering that π/3 radians is the same as 60 degrees, this evaluates to
(3/2 + 1/2) -1 = 1
This is actually the ares bounded by the two curves and the y axis. There is another
intersection of the two curves at θ = -2π/3
Plugging this value in for the lower limit results in A = 2 - (-3/2 - 1/2) = 4