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Find the area of the region bounded...

Find the area of the region bounded by parabola ` y ^(2) = 16 x ` and the line ` x = 3 `.

Text Solution

Verified by Experts

Required area = area of the region OPACQO
= 2 ( area of the region OPABO)
` = 2 int _ 0 ^(3) ydx, ` where ` y ^(2) = 16 x `, i.e., ` y = 4 sqrt x `
` = 2 int _ 0 ^(3) 4 sqrtx dx = 8 int _ 0 ^ 3 x ^((1)/(2)) dx `
` = 8 [ ( x ^((1)/(2))) /( 3//2) ]_ 0 ^(3) = ( 16) /(3) [ x ^((3)/(2)) ] _ 0 ^ 3 `
` = ( 16 ) /(3) [ 3 ^((3) /(2)) - 0 ] `
` = 16 sqrt 3 ` sq units.
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