The value of     \int_{-2}^{3}\left | 1-x^{2} \right |dx\; \; is

  • Option 1)

    7/3

  • Option 2)

    14/3

  • Option 3)

    28/3

  • Option 4)

    1/3

 

Answers (1)

As learnt in concept

Fundamental Properties of Definite integration -

If the function is continuous in (a, b ) then integration of a function a to b will be same as the sum of integrals of the same function from a to c and c to b.

\int_{b}^{a}f\left ( x \right )dx= \int_{a}^{c}f\left ( x \right )dx+\int_{c}^{b}f\left ( x \right )dx
 

- wherein

 

 

 

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

=\int_{-2}^{-1}(x^{2}-1) dx+\int_{-1}^{1}(1-x^{2}) dx+\int_{1}^{3}(x^{2}-1)dx

=\frac{-1}{3}+\frac{8}{3}-1+2-\frac{2}{3}+9-\frac{1}{3}-2

=\frac{28}{3}


Option 1)

7/3

This option is incorrect

Option 2)

14/3

This option is incorrect

Option 3)

28/3

This option is correct

Option 4)

1/3

This option is incorrect

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