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\int_{0}^{3}\left | x^{2}-x \right |dx

  • Option 1)

    53/6

  • Option 2)

    55/6

  • Option 3)

    57/6

  • Option 4)

    59/6

 

Answers (1)

best_answer

As we learnt 

 

Piece wise Continnous Function -

 

Break th function into sub intervals and calculate integrals Separately.

- wherein

If f(x) has discontinnities in \left [ a,b \right ] at finite number of points

 

 \int_{0}^{1}\left | x^{2}-x \right |dx+\int_{1}^{3}\left | x^{2}-x \right |dx

\int_{0}^{1}\left (x- x^{2} \right )dx+\int_{1}^{3}\left (x^{2}-x \right )dx

=\left [ \frac{x^{2}}{2}-\frac{x^{3}}{3} \right ]^{1}_{0}+\left [ \frac{x^{3}}{3}-\frac{x^{2}}{2} \right ]^{3}_{1}

=\frac{1}{2}-\frac{1}{3}+9-\frac{9}{2}-\frac{1}{3}+\frac{1}{2}= \frac{57}{6}

 


Option 1)

53/6

Option 2)

55/6

Option 3)

57/6

Option 4)

59/6

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gaurav

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