The area (in sq. units) of the region A = ( x , y ) : | x | + | y | ≤ 1 , 2 y 2 ≥ | x |

Required area is, A = ar O A C + ar Δ A B C ⇒ A = 4 ∫ 0 1 / 2 2 y 2 d y + 1 2 · 1 2 · 1 2 ⇒ A = 4 2 3 y 3 0 1 / 2 + 1 8 = 5 6

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 $A = \{(x, y) : | x | + | y | \leq 1, 2 y^{2} \geq | x |\}$

Answer:

Solution:

Required area is, $A = ar (O A C) + ar (Δ A B C)$

$\Rightarrow A = 4 [\int_{0}^{1 / 2} 2 y^{2} d y + \frac{1}{2} \cdot (\frac{1}{2}) \cdot (\frac{1}{2})]$

$\Rightarrow A = 4 [{(\frac{2}{3} y^{3})}_{0}^{1 / 2} + (\frac{1}{8})] = \frac{5}{6}$

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

⏱ 2mℹ️ Source: PYQ_2020

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