1.

` int _(0)^(1) xe^(x^(2))dx` is equal toA. `(1)/(2)(e+1)`B. `e-1`C. `(1)/(2)(e-1)`D. `(e^(2))/(2)`

Answer» Correct Answer - C
Let ` I = int _(0)^(1) xe^(x^(2)) dx`
Put ` x^(2) = t rArr 2x = (dt)/(dx)`
` rArr dx = (dt)/(2x)`
` :. l = int _(0)^(1) xe^(1) (dt)/(2x) = 1/2 int _(0)^(1) e^(t) dt `
` = 1/2 [ e^(t)] _(0)^(1) = 1/2 [e^(1) - e^(0) ] = 1/2 [ e-1 ] `


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