QJEEM20Ma535d: JEE Main 2020 Mathematics - Class 12 JEEM20Ma535d Solution: The area (in sq. units) of the region A = {(x, y) : (x – 1)[x]…

Question

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The area (in sq. units) of the region

A = {(x, y) : (x – 1)[x]

\leq

y

\leq

2

\sqrt{x}

, 0

\leq

x

\leq

2}, where [t]

denotes the greatest integer function, is :

Accepted Answer

y = (x – 1)[x] =

{\begin{matrix} 0, & 0 \leq x < 1 \\ x - 1, & 1 \leq x < 2 \\ 2, & x = 2 \end{matrix}

A =

\int_{0}^{2} 2 \sqrt{x} d x - \frac{1}{2} .1 .1

= 2

{[\frac{x^{3 / 2}}{\frac{3}{2}}]}_{0}^{2}

-

\frac{1}{2}

=

\frac{8 \sqrt{2}}{3} - \frac{1}{2}

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