The area (in sq. units) of the region { x ∈ R : x ≥ 0 , y ≥ 0 , y ≥ x - 2 and y ≤ x } is

y = x x = x - 2 ( x ) 2 - ( x ) - 2 = 0 ( x - 2 ) ( x + 1 ) = 0 x = 2 ⇒ x = 4 Therefore, the area of the region is ∫ 0 4 x d x - Area of ∆ A B C = 2 3 x 3 / 2 0 4 - 1 2 × 2 × 2 = 2 3 × 4 3 / 2 - 2 = 16 3 - 2 = 10 3 sq . unit

Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2018

MathematicsMediumsingle choice

The area (in sq. units) of the region ${x \in R : x \geq 0, y \geq 0, y \geq x - 2$ and $y \leq \sqrt{x}}$ is

Options:

Answer:

Solution:

$y = \sqrt{x}$

$\sqrt{x} = x - 2$

$(\sqrt{x})^{2} - (\sqrt{x}) - 2 = 0$

$(\sqrt{x} - 2) (\sqrt{x} + 1) = 0$

$\sqrt{x} = 2 \Rightarrow x = 4$
Therefore, the area of the region is
$\int_{0}^{4} \sqrt{x} d x - Area of ∆ A B C$

$= \frac{2}{3} x^{3 / 2}_{0}^{4} - \frac{1}{2} \times 2 \times 2$

$= \frac{2}{3} \times 4^{3 / 2} - 2$
$= \frac{16}{3} - 2 = \frac{10}{3} sq . unit$

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by two curves

⏱ 2mℹ️ Source: PYQ_2018

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