Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2024

MathematicsMediumnumerical

The area of the region enclosed by the parabolas $y = x^{2} - 5 x$ and $y = 7 x - x^{2}$ is

Answer:

72.00

Solution:

$y = x^{2} - 5 x$ and $y = 7 x - x^{2}$
$\int_{0}^{6} (g (x) - f (x)) d x \int_{0}^{6} ((7 x - x^{2}) - (x^{2} - 5 x)) d x \int_{0}^{6} (12 x - 2 x^{2}) d x = [12 \frac{x ^{2}}{2} - \frac{2 x ^{3}}{3}]_{0}^{6} \Rightarrow 6 (6)^{2} - \frac{2}{3} (6)^{3} = 216 - 144 = 72 unit^{2}$

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

⏱ 2mℹ️ Source: PYQ_2024

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