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int _(0)^(1) (x)/(x^(2)+1)dx |
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Answer» SOLUTION :`"Let "I= int_(0)^(1)(x)/(x^(2)+1)DX` `"Let" x^(2)+1=t rArr XDX=(dt)/(2)` `x=0 rArr t=1` `" and" x=1 rArr t=2` `:. I= int_(1)^(2) (1)/(t).(dt)/(2) =(1)/(2) int_(1)^(2) (1)/(t)dt =(1)/(2) [log |t|]_(1)^(2)` `=(1)/(2)[log |2|-log |1|]=(1)/(2)log 2.` |
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