If ∫0100f(x)dx=7,then  ∑r=1100∫01f(r-1+x)dx=

If 0100f(x)dx=7,then  r=110001f(r-1+x)dx=

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    Solution:

    r=110001f(r1+x)dx=01f(x)dx+01f(1+x)dx+01f(2+x)dx++01f(99+x)dx=01f(x)dx+12f(x)dx+23f(x)dx++99100f(x)dx=0100f(x)dx=7

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