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If f(0) = 1, f(2) = 3, f'(2) = 5 then $\int\limits_0^1x.f''(2x)dx$ is equal to: |
Zero 1 2 None of these |
2 |
$\int\limits_0^1x.f''(2x)dx=|x.\frac{f'(2x)}{2}|_0^1-\int\limits_0^11.\frac{f'(2x)}{2}dx=|x.\frac{f'(2x)}{2}-\frac{f(2x)}{4}|_0^1=\frac{f'(2x)}{2}-\frac{f(2x)}{4}+\frac{f(0)}{4}=\frac{5}{2}-\frac{3}{4}+\frac{1}{4}=2$ |
