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Question

Area lying between the curves y2 = 4x and y = 2x is
(a) 23

(b) 13

(c) 14

(d) 34

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Solution

b 13



The points of intersection of the straight line and the parabola is obtained by solving the simultaneous equations
y2=4x and y=2x⇒2x2=4x⇒4x2=4x⇒xx-1=0⇒x=0 or x=1⇒y=0 or y=2Thus O0, 0 and A1, 2 are the points of intersection of the parabola and straight lineShaded area is the required area.Using the horizontal strip method ,Shaded area =∫02x2-x1dy =∫02y2-y24 dy =12y22-14y3302 =1422 -11223-0 =1-812 =12-812 =13 sq. units

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