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Question

Value of 50(x+2x+1+x2x1)dx is

A
83
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B
163
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C
323
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D
343
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Solution

The correct option is D 343
x+(x1)=(x1)2+12+2(x1)=(x1)+1
And x2(x1)=((x1)2+12+2x1)=|(x1)1|
Then 51x+2x1+x2(x1)dx=51((x1)+1)dx+51|(x1)1|dx=51((x1)+1)dx+21(1(x1))dx+52((x1)1)dx==40(x+1)dx=10(1x)dx+41(x1)dx=[23(x32)+x]40+[x23x32]+[23x321]=323

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