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AP EAMCET20225 Jul 2022Morning ShiftMathematicsDefinite IntegrationActual

Let T>0 be a fixed number. f: R R is a continuous function such that f(x+T)=f(x), x R . If I= ₀^T f(x) d x , then ₀^ 5 T f(2 x) d x=

Options

  1. A10I
  2. B5 2 I
  3. C5I
  4. D2I

Correct answer

C. 5I

Step-by-step solution

Given, I= ₀^T f(x) d x If f(x+T)=f(x) Now, = ₀^ 5 T f(2 x) d x On putting 2 x=y d x= 1 2 d y 1 2 ₀^ 10 T f(y) d y= 10 I 2 =5 I

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