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AP EAMCET20228 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual

3 e^x-7 e^ -x 7 e^x+3 e^ -x d x=K x+L (e^ -2 x + 7 3 )+C then K+L=

Options

  1. A-3 38
  2. B21 38
  3. C38 21
  4. D-38 3

Correct answer

C. 38 21

Step-by-step solution

aligned I & = 3 e^x-7 e^ -x 7 e^x+3 e^ -x d x & =3 e^x- 7 3 e^ -x 7 e^x+3 e^ -x d x & = 3 7 7 e^x- 49 3 e^ -x 7 e^x+3 e^ -x d x & = 3 7 (7 e^x+3 e^ -x )- 58 3 e^ -x 7 e^x+3 e^ -x d x & = 3 7 d x- 3 7 58 3 e^ -x 7 e^x+3 e^ -x d x aligned I= 3 x 7 - 58 7 e^ -2 x 7+3 e^ -2 x d x Put t=7+3 e^ -2 x d t=-6 e^ -2 x d x aligned & I= 3 x 7 - 58 7 (- 1 6 ) d t t & I= 3 x 7 + 29 21 |t|+C & I= 3 x 7 + 29 21 (7+3 e^ -2 x )+C aligned aligned & K=3 / 7 and L=29 / 21 & K+L= 3 7 + 29 21 = 9+29 21 = 38 21 aligned

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