A) 2009
B) 2010
C) 2011
D) none of these
Correct Answer: C
Solution :
\[\int\limits_{0}^{a}{{{x}^{2}}f''(x)dx={{a}^{2}}f'(a)-}\]\[\int\limits_{0}^{a}{2x\,f'(x)dx={{a}^{2}}f'(a)-2[a\,f(a)-\int\limits_{0}^{a}{f(x)dx]}}\] |
\[{{a}^{2}}f'(a)-2af(a)+2\int\limits_{0}^{a}{f(x)}dx\] |
Put \[a=2010\] |
\[\int\limits_{0}^{2010}{{{x}^{2}}f''(x)}dx=2010-2+3=2011\] |
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