I do not know how the givens are useful in solving this question:
Could anyone help me please?
2026-02-25 13:35:21.1772026521
Calculating the value of a definite integral knowing the value of the integrand and its derivative on the boundaries.
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Employ integration by parts.
Note in general:
$$\int_a^b fg'=\bigg[fg\bigg]_a^b-\int_a^b f'g$$
Thus, let $f=x$ and $g'=p''(x)$
$$\therefore \int_0^2 xp''(x)dx=\bigg[xp'(x)\bigg]_0^2-\int_0^2 p'(x)$$
$$=2p'(2)-(p(2)-p(0))=2(-1)-(3-3)=-2$$