\int_{0}^{\sqrt{2}}\left [ x^{2} \right ]dx\; is

  • Option 1)

    2-\sqrt{2}\;

  • Option 2)

    \; \; 2+\sqrt{2}\; \; \; \;

  • Option 3)

    \sqrt{2}-1\; \;

  • Option 4)

    \; \sqrt{2}-2\;

 

Answers (1)

 

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_{0}^{2}[x^{2}]dx

\int_{0}^{1}[x^{2}]dx + \int_{0}^{\sqrt{2}}[x^{2}]dx

=\int_{0}^{1}0\ dx + \int_{0}^21\ dx=(\sqrt{2}-1) 


Option 1)

2-\sqrt{2}\;

This is incorrect option

Option 2)

\; \; 2+\sqrt{2}\; \; \; \;

This is incorrect option

Option 3)

\sqrt{2}-1\; \;

This is correct option

Option 4)

\; \sqrt{2}-2\;

This is incorrect option

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