1.

`int _(3)^(8) (2-3x)/(xsqrt(1+x))dx` is equal toA. `2log((3)/(2e^(3)))`B. `log((3)/(e^(3)))`C. `4log((3)/(e^(3)))`D. None of these

Answer» Correct Answer - A
Let ` l = int _(3)^(a) (2-3x)/(xsqrt(1+x))dx `
Put ` 1+ x = t^(2) rArr dx = 2 t dt `
When x = 3, t= 2
and x = 8, t=3
` :. l = 2 int _(2)^(3) (5- 3t^(2))/(t^(2)-1) dt = 2int_(2)^(3) (2/(t^(2)-1)-3) dt`
` = 2 [ 2/(2.1) log ((t-1)/(t+1)) - 3t ]_(2)^(3) = 2 log (3/(2e^(3)))`


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