The area (in sq. units) of the region A = { ( x , y ) : ( x - 1 ) [ x ] ≤ y ≤ 2 x , 0 ≤ x ≤ 2 } , where [ t ] denotes the greatest integer function, is :

y = [ x ] ( x - 1 ) = 0 0 ≤ x < 1 x - 1 1 ≤ x < 2 Area = ∫ 0 2 2 x · d x - 1 2 ( 1 ) ( 1 ) = 4 x 3 / 2 3 0 2 - 1 2 = 8 2 3 - 1 2

Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesHard2 minPYQ_2020

MathematicsHardsingle choice

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 :

Options:

Answer:

Solution:

$y = [x] (x - 1)$
$= \{\begin{matrix} 0 & 0 \leq x < 1 \\ x - 1 & 1 \leq x < 2 \end{matrix}$

Area $= \int_{0}^{2} 2 \sqrt{x} \cdot d x - \frac{1}{2} (1) (1) = {(\frac{4 x^{3 / 2}}{3})}_{0}^{2} - \frac{1}{2} = \frac{8 \sqrt{2}}{3} - \frac{1}{2}$

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by Miscellaneous Curves

⏱ 2mℹ️ Source: PYQ_2020

Doubts & Discussion

Loading discussions...