`int_(0)^(1)x. e^(2x)dx` का मान ज्ञात कीजिए।

Explanation

`int_(0)^(1)x.e^(2x)dx`
`=[x.(e^(2x))/(2)]_(0)^(1)-int_(0)^(1)1.(e^(2x))/(2)dx`
`=(1)/(2)[e^(2)-1]-(1)/(4)[e^(2x)]_(0)^(1)`
`=(1)/(2)e^(2)-(1)/(4)(e^(2)-1)`
`=(1)/(4)e^(2)+(1)/(4)=(1)/(4)(e^(2)+1)`