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AP EAMCET202021 Sep 2020Evening ShiftMathematicsIndefinite IntegrationActual

Suppose that (f ) and (g ) are integrable on ([a, b] ), then (f+g ) is integrable on ......... .

Options

  1. A((a, b) )
  2. BCannot comment
  3. C([a, b] )
  4. DRange of (f+g )

Correct answer

C. ([a, b] )

Step-by-step solution

As (f ) and (g ) are integrable on ([a, b] ), then ( _ x₁ ^ x₂ f(x) d x ) and ( _ x₁ ^ x₂ g(x) d x ) exists for every value of (x₁, x₂ [a, b] ), then ( _ x₁ ^ x₂ f(x) d x+ _ x₁ ^ x₂ g(x) d x= _ x₁ ^ x₂ (f+g)(x) d x ) Also exists for ( x₁, x₂ [a, b] ) Hence, option (c) is correct.

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