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प्रश्न
Evaluate the definite integral:
`int_0^1 x e^(x^2) dx`
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उत्तर
Putting `x^2 = t`
`x dx = 1/2 dt`
`= 1/2 int e^t dt`
`= e^t/2 = e^(x^2)/2`
`= int_0^1 xe^(x^2) dx = 1/2 [e^(x^2)]_0^1`
`= 1/2 [e^t - e^0] = 1/2 (e - 1)`
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