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Evaluate the following definite integral...

Evaluate the following definite integral: `int_1^2logx\ dx`

Text Solution

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`int_(1)^(2)log x dx=int_(1)^(2)(logx)(1)dx`
`=[(logx)int1 dx]_(1)^(2)-int_(1)^(2)[(d)/(dx)(logx)int 1dx]dx`
`=[(logx)x]_(1)^(2)-int_(1)^(2)(1)/(x)xx x dx`
`=[xlogx]_(1)^(2)-int_(1)^(2)1dx`
`=(2log 2-1 .log 1)-[x]_(1)^(2)`
`=(log 4-0)-(2-1)" ..."[because log 1=0]`
`=log 4-1.`
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