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Find the area of the region bounde...

Find the area of the region bounded by the curve ` x^(2) = 16 y `, lines ` y = 2, y = 6 ` and Y - axis lying in the first quadrant.

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Required area ` = int _ 2 ^ 6 x dy` , where ` x ^ 2 = 16 y `
` = int _ 2 ^ 6 sqrt ( 16 y ) dy `
` = 4 int _ 2 ^ 6 y ^ ((1) /(2)) dy = 4 * [ ( y ^ ((3)/2)) /( 3//2) ] _ 2 ^ 6 `
` ( 8 ) /(3) [ 6 ^ ((3 ) /(2)) - 2 ^((3)/(2)) ] ` sq units.
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