The area (in sq. units) of the region { x ∈ R : x ≥ 0 , y ≥ 0 , y ≥ x − 2 and y ≤ x } , is

The intersection point of y = x − 2 and y = x is ( 4 , 2 ) . The required area = ∫ 0 4 x d x − 2 1 × 2 × 2 = 3 16 − 2 = 3 10

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MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesMedium2 minPYQ_2018

MathematicsMediumsingle choice

The area (in sq. units) of the region ${x \in R : x \geq 0, y \geq 0, y \geq x - 2$ and $y \leq x}$ , is

Question diagram: The area (in sq. units) of the region { x ∈ R : x ≥ 0 , y ≥

Options:

Answer:

Solution:

The intersection point of $y = x - 2$ and $y = x$ is $(4, 2)$ . The required area $= \int_{0}^{4} x d x - \frac{1}{2} \times 2 \times 2 = \frac{16}{3} - 2 = \frac{10}{3}$

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

⏱ 2mℹ️ Source: PYQ_2018

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