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COMEDK2020MathematicsDefinite Integration

If k ₀¹ x f(3 x) d x= ₀³ t f(t) d t , then the value of k is

Options

  1. A3
  2. B9
  3. C1 / 3
  4. D1 / 9

Correct answer

B. 9

Step-by-step solution

Let I= ₀³ t f(t) Put t=3 x d t=3 d x When t=0 x=0 and t=3 x=1 aligned I &= ₀¹ 3 x f(3 x)(3 d x) &=9 ₀¹ x f(3 x) d x &=k ₀¹ x f(3 x) d x k &=9 aligned

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