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NDA2016MathematicsDefinite IntegrationActual

If _ -2 ^5 f(x) d x=4 and ₀^5 1+f(x) d x=7 , then what is _ -2 ^0 f(x) d x equal to?

Options

  1. A–3
  2. B2
  3. C3
  4. D5

Correct answer

B. 2

Step-by-step solution

aligned & _ -2 ^5 f(x) d x=4 and ₀^5 1+f(x) d x=7 & ₀^5 f(x) d x=7- ₀^5 1 d x=7-5=2 ...(1) & _ -2 ^0 f(x) d x= ? & _ -2 ^0 f(x) d x+ ₀^5 f(x) d x=4 & _ -2 ^0 f(x) d x=4- ₀^5 f(x) d x & =4-2=2 . [Using eqn. (1)] & _ -2 ^0 f(x) d x=2 aligned

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