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MHT CET20226 Aug 2022Morning ShiftMathematicsIndefinite IntegrationActual

If f(x)= 5 x^8+7 x^6 (x^2+1+2 x^7 )^2 d x, x 0 and f(0)=0 , then value of f(1) is

Options

  1. A- 1 2
  2. B1 4
  3. C- 1 4
  4. D1 2

Correct answer

B. 1 4

Step-by-step solution

aligned & f(x)= 5 x^8+7 x^6 (x^2+1+2 x^7 )^2 d x & = 5 x^8+7 x^6 x¹⁴ ( 1 x^5 + 1 x^7 +2 )^2 d x & = 5 x⁻⁶+7 x⁻⁸ ( 1 x^5 + 1 x^7 +2 )^2 d x & =- d t t^2 [ where t= 1 x^5 + 1 x^7 +2 ] & = 1 t +C aligned aligned & = 1 ( 1 x^5 + 1 x^7 +2 ) +C & f(x)= x^7 x^2+1+2 x^7 +C & f(0)=0 c=0 i.e. f(x)= x^7 x^2+1+2 x^7 & f(1)= 1 4 aligned

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