1.

int_(0)^(1)x e^(x^(2)) dx

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Solution :`" LET I=" int_(0)^(1) xe^(x^(2))dx`
`"Let "x^(2)=trArr 2x=(DT)/(dx) rArr XD x= (dt)/(2)`
`x=0rArr t=0 `
`"and " x=1 rArrt=1`
` :, I=(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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