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KCET2021MathematicsDefinite Integration

The value of ₀⁴⁰⁴² x d x x + 4042-x is equal to

Options

  1. A4042
  2. B2021
  3. C8084
  4. D1010

Correct answer

B. 2021

Step-by-step solution

Let I= ₀⁴⁰⁴² x x + 4042-x d x...(i) Using the property, ₀^ a f(x) d x= ₀^ a f(a-x) d xI= ₀⁴⁰⁴² 4042-x 4042-x + x ...(ii) Adding Eqs. (i) and (ii), 2 I= ₀⁴⁰⁴² x + 4042-x 4042-x + x d x 2 I= ₀⁴⁰⁴² 1 d x 2 I=4042 I=2021

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