Maths-
General
Easy

Question

Let g(x) be a function defined on [0, 7] and g(x) = stretchy integral subscript 0 end subscript superscript x end superscript   f left parenthesis t right parenthesis d t where f is the function whose graph is as shown in figure given below, then

M is same as obtained in above question. If at x = a and x = b, g(x) attains its greatest value and least values respectively, then
a b =

  1. m 6    
  2. m 1    
  3. m 9    
  4. - m    

The correct answer is: - m


    g to the power of ´ end exponent left parenthesis x right parenthesis equals 0 rightwards double arrow f left parenthesis x right parenthesis equals 0
    x equals 37
    g open parentheses 3 close parentheses equals stretchy integral subscript 0 end subscript superscript 3 end superscript   f open parentheses x close parentheses d x
    equals left parenthesis 1 cross times 2 right parenthesis plus fraction numerator 1 over denominator 2 end fraction left parenthesis 2 plus 4 right parenthesis plus fraction numerator 1 over denominator 2 end fraction cross times 1 cross times 4
    equals 2 plus 3 plus 2
    equals 7
    g left parenthesis 7 right parenthesis equals stretchy integral subscript 0 end subscript superscript 7 end superscript   f left parenthesis x right parenthesis d x
    equals 7 minus open parentheses fraction numerator 1 over denominator 2 end fraction cross times 2 cross times 4 plus left parenthesis 4 cross times 1 right parenthesis plus fraction numerator 1 over denominator 2 end fraction cross times 1 cross times 4 close parentheses
    equals 7 minus open parentheses 10 close parentheses
    equals negative 3
    a equals 3 comma b equals 7
    a minus b equals negative 4

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