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Question

Let f(x)=max{x2,(1x)2,2x(1x)}, where 0x1 the area of the region bounded by the curve y=f(x) between x[0,13],[13,23],[23,1] and xaxis represented by S1,S2,S3 then

A
S1,S2,S3 are in G.P
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B
S1,S2,S3 are in H.P
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C
S1=S3
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D
S1+S2+S3=1727
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Solution

The correct options are
C S1=S3
D S1+S2+S3=1727
S1=∣ ∣130(1x)2dx∣ ∣
=∣ ∣[13(1x)3]130∣ ∣
=13{8271}
=1981
S2=∣ ∣23132x(1x)dx∣ ∣
=x22x332313
=(491681)(19281)
=391481=1381
and S3=∣ ∣123x2dx∣ ∣
=13(1827)=1981
Hence, S1=S3=1981
and S2=1381
S1+S2+S3=1981+1381+1981=5181=1727
957064_1048511_ans_ffe46254ae6e4811bcd8dcc1d29949a7.png

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