The area bounded by the curves y = ( x − 1 ) 2 , y = ( x + 1 ) 2 and y = 4 1 is

Required area = 2 ∫ 0 2 1 [ ( x − 1 ) 2 − 4 1 ] d x = 2 [ 3 ( x − 1 ) 3 ] 0 2 1 − 2 1 [ x ] 0 2 1 = 3 2 ( − 8 1 + 1 ) − 2 1 ( 2 1 − 0 ) = 3 1 sq. units

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesHard2 minPYQ_2023

MathematicsHardsingle choice

The area bounded by the curves $y = (x - 1)^{2}$ , $y = (x + 1)^{2}$ and $y = \frac{1}{4}$ is

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Answer:

Solution:

$Required area = 2 \int_{0}^{\frac{1}{2}} [(x - 1)^{2} - \frac{1}{4}] d x = 2 [\frac{( x - 1 ) ^{3}}{3}]_{0}^{\frac{1}{2}} - \frac{1}{2} [x]_{0}^{\frac{1}{2}} = \frac{2}{3} (- \frac{1}{8} + 1) - \frac{1}{2} (\frac{1}{2} - 0) = \frac{1}{3} sq. units$

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

⏱ 2mℹ️ Source: PYQ_2023

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