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If for n=4, the approximate value of integral not stretchy integral subscript 1 end subscript superscript 9 end superscript x to the power of 2 end exponent d xby Trapezoidal rule is 2 open square brackets fraction numerator 1 over denominator 2 end fraction left parenthesis 1 plus 9 to the power of 2 end exponent right parenthesis plus alpha to the power of 2 end exponent plus beta to the power of 2 end exponent plus 7 to the power of 2 end exponent close square brackets, then

  1. alpha equals 1 comma   beta equals 3    
  2. alpha equals 2 comma   beta equals 4    
  3. alpha equals 3 comma   beta equals 5    
  4. alpha equals 4 comma   beta equals 6    

The correct answer is: alpha equals 3 comma   beta equals 5


    fraction numerator 8 over denominator 4 end fraction equals 2

    therefore not stretchy integral subscript 1 end subscript superscript 9 end superscript x to the power of 2 end exponent d x equals fraction numerator h over denominator 2 end fraction open square brackets open parentheses y subscript 0 end subscript plus y subscript n end subscript close parentheses plus 2 left parenthesis y subscript 1 end subscript plus y subscript 2 end subscript..... plus y subscript negative 1 end subscript right parenthesis close square brackets
    equals fraction numerator 2 over denominator 2 end fraction open square brackets left parenthesis 1 to the power of 2 end exponent plus 9 to the power of 2 end exponent right parenthesis plus 2 left parenthesis 3 to the power of 2 end exponent plus 5 to the power of 2 end exponent plus 7 to the power of 2 end exponent right parenthesis close square brackets
    equals 2 open square brackets fraction numerator 1 over denominator 2 end fraction left parenthesis 1 plus 9 to the power of 2 end exponent right parenthesis plus 3 to the power of 2 end exponent plus 5 to the power of 2 end exponent plus 7 to the power of 2 end exponent right parenthesis close square brackets
    Clearly, from above equationalpha equals 3 comma beta equals 5.

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