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JEE Main20245 Apr 2024Morning ShiftMathematicsDefinite IntegrationActual

The integral ₀^ / 4 136 x 3 x+5 x d x is equal to :

Options

  1. A3 -50 _e 2+20 _e 5
  2. B3 -25 _e 2+10 _e 5
  3. C3 -10 _e(2 2 )+10 _e 5
  4. D3 -30 _e 2+20 _e 5

Correct answer

A. 3 -50 _e 2+20 _e 5

Step-by-step solution

aligned & I= ₀^ / 4 136 x 3 x+5 x d x & 136 x=A(3 x+5 x)+B(3 x-5 x) & 136=3 A-5 B...(i) & 0=5 A+3 B...(ii) aligned aligned & 3 ~B =-5 ~A B =- 5 3 ~A & 136=3 ~A -5 (- 5 3 ~A ) & 136=3 ~A + 25 3 ~A & 136= 34 ~A 3 & A = 136 3 34 =12 & ~B = -5 3 (12)=-20 aligned aligned & I= ₀^ / 4 A(3 x+5 x) 3 x+5 x + ₀^ / 4 B(3 x-5 x) 3 x+5 x & =A(x)₀^ / 4 +B[ (3 x+5 x)]₀^ / 4 & =12 ( 4 )-20 ( 3 2 + 5 2 )- (0+5) & =3 -20 4 2 +20 5 & =3 -20 5 2 2+20 5 & =3 -50 2+20 5 aligned

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