The area (in sq. units) of the region x , y ∈ R 2 : x 2 ≤ y ≤ 3 - 2 x , is.

Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2020

MathematicsMediumsingle choice

The area (in sq. units) of the region $\{(x, y) \in R^{2} : x^{2} \leq y \leq 3 - 2 x\}$ , is.

Answer:

Solution:

Point of intersection of $y = x^{2} & y = - 2 x + 3$ , is obtained by $x^{2} + 2 x - 3 = 0$ $⟹ x = - 3, 1$ .

So, area of the required region is

$\int_{- 3}^{1} ((3 - 2 x) - x^{2}) d x$

$= {[3 x - x^{2} - \frac{x^{3}}{3}]}_{- 3}^{1} = \frac{32}{3}$ .

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

⏱ 2mℹ️ Source: PYQ_2020

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