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AP EAMCET202018 Sep 2020Morning ShiftMathematicsDefinite IntegrationActual

Find the value of ' (k ) ', if it is given that ( ₀^ b-c f(x+c) d x=k _c^b f(x) d x )

Options

  1. A1
  2. B2
  3. C0
  4. D-2

Correct answer

A. 1

Step-by-step solution

(I= ₀^ b-c f(x+c) d x ) Put (x+c=t ), then at (x=0, t=c ) and at (x=b-c, t=b ) and (d x=d t ), so (I= _c^b f(t) d t= _c^b f(x) d x ₀^b f(x+c) d x= _c^b f(x) d x ) Therefore (k=1 )

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