The area bounded by y − 1 = ∣ x ∣ , y = 0 and ∣ x ∣ = 2 1 will be:

The given lines are, y − 1 = x , x ≥ 0 ; y − 1 = − x , x < 0 y = 0 ; x = − 2 1 , x < 0 ; x = 2 1 , x ≥ 0 so that the area bounded is as shown in the figure. Required area = 2 ∫ 0 1/2 ( 1 + x ) d x = 2 ( x + 2 x 2 ) 0 1/2 = 2 ( 2 1 + 8 1 ) = 4 5

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea of Curve along axisMedium2 minPYQ_2017

MathematicsMediumsingle choice

The area bounded by $y - 1 = ∣ x ∣, y = 0$ and $∣ x ∣ = \frac{1}{2}$ will be:

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Answer:

Solution:

The given lines are, $y - 1 = x, x \geq 0; y - 1 = - x, x < 0 y = 0; x = - \frac{1}{2}, x < 0; x = \frac{1}{2}, x \geq 0$ so that the area bounded is as shown in the figure.
$Required area = 2 \int_{0}^{1/2} (1 + x) d x = 2 (x + \frac{x ^{2}}{2})_{0}^{1/2} = 2 (\frac{1}{2} + \frac{1}{8}) = \frac{5}{4}$

Stream:VITEEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area of Curve along axis

⏱ 2mℹ️ Source: PYQ_2017

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