If f(x) is differentiable and ∫0t2 xf(x)dx=25t5, then f425 equals

If f(x) is differentiable and 0t2xf(x)dx=25t5, then f425 equals

  1. A

    2/5

  2. B

    -5/2

  3. C

    1

  4. D

    5/2

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    Solution:

    We have,

         0t2xf(x)dx=25t5ddt0t2xf(x)dx=ddt25t5

     2t×t2ft2=2t4                  [Using Leibnitz's rule]

    ft2=tf425=25

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