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NDA2024MathematicsDefinite IntegrationActual

Let p= _a^b f(x) d x and q= _a^b|f(x)| d x . If f(x)=e^ -x , then which one of the following is correct?

Options

  1. Ap=2 q
  2. Bp=-q
  3. C4 p=q
  4. Dp=q

Correct answer

D. p=q

Step-by-step solution

p= _a^b f(x) d x and q= _a^b|f(x)| d x aligned f(x) & =e^ -x is always + ve x R e^ -x & = |e^ -x | aligned |f(x)|= |e^ -x |=e^ -x =f(x) _a^b f(x) d x= _a^b|f(x)| d x Hence, p=q

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