इन समाकलनो का मान ज्ञात कीजिएः
`int_(0)^(1) {xe^(x)+sin""(pix)/(4)}dx`

Explanation

यहाँ `underset(0)overset(1)int {xe^(x)+sin""(pix)/(4)}dx`
`underset(0)overset(1)int underset(I)(x)" "underset(II)e^x+ underset(0)overset(1)int sin""(pi//4)/(4)dx`
`=xunderset(0)overset(1)int e^(x)dx+ underset(0)overset(1)int 1.e^(x)dx+[-(cos pix)/((pi/4))]_(0)^(1)`
`=[xe^(x)]_(0)^(1)+[e^(x)]_(0)^(1)-4/pi [cos""(pix)/(4)]_(0)^(1)`
`=(1.e-0)-(e-1)-4/pi[cos""(pix)/(4)]`
`=1-4/pi[cos""(pi)/(4)-cos 0]`
`=1-4/pi[1/sqrt2-1]`
`=1+4/pi-(2sqrt2)/(pi)`