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  • Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Very short answer type question 44

Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Very short answer type question 44

Answers (1)

Answer: \sqrt{2}-1

Hint: The values of greatest integer function when 0<x<1,[x]=0 

        And when 1<x<2,[x]=1

Given: \int_{0}^{\sqrt{2}}\left[x^{2}\right] d x

Solution:  \int_{0}^{\sqrt{2}}\left[x^{2}\right] d x

=\int_{0}^{1}\left[x^{2}\right] d x+\int_{1}^{\sqrt{2}}\left[x^{2}\right] d x        [ using the value of greatest integer function ]

\begin{aligned} &=0+\int_{1}^{\sqrt{2}} 1 d x \\\\ &=[x]_{1}^{\sqrt{2}} \\\\ &=\sqrt{2}-1 \end{aligned}

Note: Final answer is not matching with the book.

 

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