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Question
Find the area of the region bounded by the parabolas y2 = 6x and x2 = 6y.
Solution
The intersecting points of the given parabolas are obtained by solving these equations for x and y
Which are 0(0, 0) and (6, 6).
Hence Area OABC = `int_0^6 (sqrt(6x) - x^2/6) "d"x`
= `|2sqrt(6) x^(3/2)/3 - x^3/18|_0^6`
= `2sqrt(6) (6)^(3/2)/3 - (6)^3/18`
= 12 sq.units
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