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JEE Advanced2006MathematicsDefinite IntegrationActual

Paragraph: Read the following passage and answer the questions. For every function f(x) which is twice differentiable, these will be good approximation of _a^b f(x) d x ( b-a 2 ) f(a)+f(b) . Now, if we take c= a+b 2 , then using above again, we get _a^b f(x) d x= _a^c f(x) d x+ _c^b f(x) d x b-a 4 f(a)+f(b)+2 f(c) and so on. We get approximation for value of _a^b f(x) d x . Question: Good approximation of ₀^ / 2 x d

Options

  1. A4
  2. B4 ( 2 +1)
  3. C8 ( 2 +1)
  4. D8

Correct answer

C. 8 ( 2 +1)

Step-by-step solution

₀^ / 2 x d x= 2 -0 4 ( 0+ ( 2 )+2 ( 0+ 2 2 ) )= 8 (1+ 2 ) .

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