Let $f$ be a function with $f(0) = 9$, $f(4) = 7$, and $f '(4) = 3$. Evaluate the integral $$\int_{0}^{4}xf''(x)dx$$
I tried to solve it using a method my teacher showed to us in class but it involved a huge table of values. I feel like there is missing information.
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$\begingroup$Hint: Use integration by parts to get $\displaystyle\int_{0}^{4}xf''(x)\,dx = \left[xf'(x)\right]_{0}^{4} - \int_{0}^{4}f'(x)\,dx$.
Evaluating $xf'(x)$ at $x = 0$ and $x = 4$ is doable from the data you are given.
Also, $\displaystyle\int_{0}^{4}f'(x)\,dx$ should be fairly simple to integrate.
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