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AP EAMCET20226 Jul 2022Evening ShiftMathematicsDefinite IntegrationActual

If f is continuous function and f(x+T)=f(x), x R , it is given that ₀^ N T f(t) d t=N ₀^T f(t) d t (N is natural number). Then, ₀^ 50 1- 2 x d x=

Options

  1. A50 2
  2. B100 2
  3. C50 2
  4. D100 2

Correct answer

B. 100 2

Step-by-step solution

Let aligned I= & ₀^ 50 1- 2 x d x = & 50 ₀^ 1- 2 x d x & [ 1- 2(2 +x) = 1- 2 x ] I= & 50 ₀^ 2 x d x & =50 2 [- x]₀^ & =-50 2 [(-1)-1]=100 2 aligned

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