1.

Let P(x) be a polynomial of degree n with leading coefficient 1. Let v (x) be any function and v_(1)(x) = int v (x) dx, v_(2)(x)=intv_(1)(x)dx...v_(n+1)=intv_(n)(x)dx. then int P(x) v(x) dx is equal to

Answer»

<P>`P(X)v_(1)(x)+(p'(x)v_(2)(x))/(2!)+(P''(x)v_(3)(x))/(3!)...+(v_(n+1)(x))((n+1)!)`/
`P(x)v_(1)(x)-P(x)v_(2)(x)+P''(x)v_(3)(x)...+(-1)^(n)n!v_(n+1)(x)`
`P(x)v_(1)(x)+P'(x)v_(2)+P''(x)v_(3)(x)...+nv_(n)+1(x)`
`P(x)v_(1)(x)-(p'(x)v_(2)(x))/(2!)+(P''(x)v_(3)(x))/(3!)...+(-1)^(n)(v_(n+1)(x))/((n+1))!`

Answer :B


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