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Area bounded by the parabola 2y= $x^2$ and the line x = y-4 is equal to
(a) 4.5
(b) 9
(c) 18
(d) 36
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Answer is 18.
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Answer is  18 sq units.

2y = x^2 and x = y - 4 ....... eqA

Now,

x^2 = 2 ( x + 4 ) ......eq2

Solving  eq2 we get x = 4 , - 2.

Place Values of x in eqA we get y = 8 , 2.

Thus, the points of intersection are (8, 4), (2, –2)

Area = Integration from -2 to 4 on ( x - ( x^2 / 2 ) + 4 ) dx

Solve Integration we get Answer as 18
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