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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» <html><body><p><<a href="https://interviewquestions.tuteehub.com/tag/p-588962" style="font-weight:bold;" target="_blank" title="Click to know more about P">P</a>>`P(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>)v_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)(x)+(p'(x)v_(2)(x))/(2!)+(P''(x)v_(3)(x))/(3!)...+(v_(n+1)(x))((n+1)!)`/<br/>`P(x)v_(1)(x)-P(x)v_(2)(x)+P''(x)v_(3)(x)...+(-1)^(n)n!v_(n+1)(x)`<br/>`P(x)v_(1)(x)+P'(x)v_(2)+P''(x)v_(3)(x)...+nv_(n)+1(x)`<br/>`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))!`</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html> | |