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AP EAMCET202125 Aug 2021Morning ShiftMathematicsDefinite IntegrationActual

If _a^b x^3 d x=0 and _a^b x^2 d x= 2 3 , then

Options

  1. Aa=-1 and b=1
  2. Ba=1 and b=-1
  3. Ca=2 and b=-2
  4. Da=-2 and b=2

Correct answer

A. a=-1 and b=1

Step-by-step solution

We have, aligned & _a^b x^3 d x=0 & [ x^4 4 ]_a^b=0 b^4-a^4=0 & b=-a, b a & and _a^b x^2 d x= 2 3 & [ x^3 3 ]_a^b= 2 3 & b^3-a^3=2 & -a^3-a^3=2 & aligned array ll & a^3=-1 & a=-1 & b=-a=1 array

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