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Q.

If the line x=α divides the area of region R=(x,y)∈R2:x3≤y≤x,0≤x≤1 into two equal parts then

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a

0<α≤12

b

2α4−4α2+1=0

c

α4+4α2−1=0

d

12<α<1

answer is B.

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Detailed Solution

2∫0αx−x3 dx = ∫01x−x3 dx2α22− α44 = 12 −142α4− 4α2+1=0α2=4±224 ⇒α2=1-12 ⇒12<α<1

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