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Manipal MET2016MathematicsIndefinite Integration

^ -3 / 7 x ^ -11 / 7 x d x is equal to

Options

  1. A| ^ 4 / 7 x |+C
  2. B4 7 ^ 4 / 7 x+C
  3. C-7 4 ^ -4 / 7 x+C
  4. D| ^ 3 / 7 x |+C

Correct answer

C. -7 4 ^ -4 / 7 x+C

Step-by-step solution

m+n=- 3 7 + ( -11 7 )=-2(- ve integer ) Let I= ^ -3 / 7 x ( ^ (-2+ 3 7 ) x ) d x aligned & = ^ -3 / 7 x ⁻² x ^ 3 / 7 x d x & = cosec ^2 x ( ^ 3 / 7 x ^ 3 / 7 x ) d x= cosec ^2 x d x ^ 3 / 7 x aligned Put x=t - cosec ^2 x d x=d t I=- d t t^ 3 / 7 =- t^ 3 7 +1 - 3 7 +1 +C aligned & =- 7 4 t^ 4 / 7 +c=- 7 4 ^ 4 / 7 x+C & =- 7 4 ^ -4 / 7 x+C aligned

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