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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Which of the following definite integral vanishes?

Options

  1. A_ - ^ ( 2 x 2^2 x 2^3 x 2^4 x 2^5 x ) d x
  2. B_ -1 ^1 (x+ x^2+1 ) d x
  3. C₀^1 ⁻¹ ( 2 x-1 1+x+x^2 ) d x
  4. D₀^ / 2 ( x) d x

Correct answer

D. ₀^ / 2 ( x) d x

Step-by-step solution

(1) I= _ - ^ ( 2 x 2^2 x 2^3 x 2^4 x 2^5 x ) _ f(x) d xI=2 ₀^ f(x) d x [f(x) is given ]I=2 2 ₀^ 2 f(x) d x (using Queen) I=4 ₀^ 2 f(x) d x=4 I₁ Now, I₁= ₀^ 2 f(x) d x Using King aligned & I₁=-I₁ & I₁=0 & I=0 aligned

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