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I have no clue as to what has to be done for this problem. Any help would be appreciated.

Assume that f is a function with a continuous second derivative f''(x) and suppose that f(1) = 2; f(4) = 6; f'(1) = 3 and f'(4) = 5.

Evaluate integrate from 1 to 4 of xf''(x)dx

Use integration by parts

Sxf'' = xf' - Sf' = xf' - f

so , an anti-derivative for xf'' is xf' - f

Sxf'' from 1 to 4 is therefore

(4f'(4) - f(4)) - (1f'(1) - f(1)) =

((4)(5) - 6) - ((1)(3) - (2)) =

(20 - 6) - (3 - 2) =

14 - 1 =

13

The answer is 13

Calculus

Answers by Expert:

I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.

Ph.D. in Mathematics and many years teaching Calculus at state universities.**Education/Credentials**

B.S. , M.S. , Ph.D.