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Find the area of the smaller region boun...

Find the area of the smaller region bounded by the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and the straight line `x/a+y/b=1.`

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The area of the smaller region bounded by the ellipse `x^2/a^2​+y^2/b^2​=1` and the line x/a​+y/b​=1 is
∴Area BACB=Area (OBCAO)−Area(OBAO)
=`∫_0^a b√1--x^2/a^2 dx-∫_0^a b(1-x)/a dx`
=`b/a∫_0^a √a^2-x^2dx-∫_0^a b/a(a-x) dx`
=`b/a[{∫_0^a x/2√a^2-x^2 +a^2/2 sin^(-1)⁡x/a}-{∫_0^a (ax-x^2/2)} `
=`b/a​[a^2π/4​−a^2/2​]`
=`(ba^2)/(2a)​[π/2​−1]`
=`ab/2​[π/2​−1]`
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