Let S = { ( x , y ) ; x ( 3 x − 2 ) y ( 3 x − 1 ) < 0 } and S ′ = {( x , y ) ∈ R 2 : − 1 < x < 1 , − 1 < y < 1 } . Find the area of S ∩ S ′ .

Case-I : when y 0 Case-II : when y > 0 , then x ( 3 x − 2 ) ( 3 x − 1 ) < 0 x ∈ ( − 1 , 0 ) ∪ ( 3 1 , 3 2 ) 1 + 3 1 × 3 = 2

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesMedium2 minQB

MathematicsMediuminteger

Let $S = {(x, y); \frac{y ( 3 x - 1 )}{x ( 3 x - 2 )} < 0}$ $and S^{'} = {(x, y) \in R^{2} : - 1 < x < 1, - 1 < y < 1} . Find the area of S \cap S^{'} .$

Answer:

Solution:

Case-I : when $y < 0$ , then $\frac{3 x - 1}{x ( 3 x - 2 )} > 0$

Case-II : when $y > 0$ , then $\frac{( 3 x - 1 )}{x ( 3 x - 2 )} < 0$ $x \in (- 1, 0) \cup (\frac{1}{3}, \frac{2}{3})$

$1 + \frac{1}{3} \times 3 = 2$

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

⏱ 2mℹ️ Source: QB

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