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KCET2009MathematicsDefinite Integration

₁³ 4- x x + 4- x dx is equal to

Options

  1. A1
  2. B3
  3. C2
  4. D0

Correct answer

A. 1

Step-by-step solution

Let I= ₁³ 4-x x + 4-x d x ...(i) I= ₁³ 4-(4-x) 4-x + 4-(4-x) d x gathered [ _ a ^ b f(x) d x= _ a ^ b f(a+b-x) d x ] I= ₁³ x 4-x + x d x ...(ii) gathered On adding Eqs. (i) and (ii), we get aligned 2 I &= ₁³ 1 dx =[ x ]₁³ I &= 2 2 =1 aligned

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