Q15 of 25 Page 8

In the figure shown below, AOBA is the part of the ellipse 9x2 + y2 = 36 in the first quadrant such that OA = 2 and OB = 6. Find the area between the arc AB and the chord AB.


Given; 9x2 + y2 = 36



The equation of AB is;


⇒ y = 6 − 3x


Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x = a and x=b, where f(x) is a continuous function defined on [a,b], is given by .


∴ Required Area




=3π − 12 + 6 − 0 − 0 + 0 − 0


= 3π − 6


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