Q. 195.0( 1 Vote )

Draw a rough sketch of the region {(x, y) : y2 ≤ 6ax and x2 + y2 ≤ 16a2}. Also find the area of the region sketched using method of integration.

Answer :

Given;

The region {(x, y) : y2 ≤ 6ax and x2 + y2 ≤ 16a2}



By solving the equations: y2 ≤ 6ax and x2 + y2 ≤ 16a2


Through substituting for y2


x2 + 6ax = 16a2


(x − 2a) (x + 8a) = 0


x = 2a.


[as x = -8a is not possible]


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 .


[By the symmetry of the image w.r.t x axis]



Required area =





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