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NDA2023MathematicsDefinite IntegrationActual

Let I= _ -2 ^ 2 ^4 x+ ^4 x 1+3^x d x What is ₀^ ( ^4 x+ ^4 x ) d x equal to?

Options

  1. A3 8
  2. B3 4
  3. C3 2
  4. D3

Correct answer

B. 3 4

Step-by-step solution

aligned & Since, ₀^ ( ^4 x+ ^4 x ) d x & = ₀^ ( ( ^2 x+ ^2 x )^2-2 ^2 x ^2 x ) d x & = ₀^ (1- ^2 2 x 2 ) d x= ₀^ (1- 1- 4 x 4 ) d x & = 1 4 ₀^ (3+ 4 x) d x= 1 4 (3 x+ 4 x 4 )₀^ = 3 4 aligned

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