Let R = { x , y : x 2 + y 2 ≤ 144 and sin ( x + y ) ≥ 0 } . And S be the area of region given by R , then find S /9 π .

x 2 + y 2 ≤ 144 and sin ( x + y ) ≥ 0 ⇒ 2 nπ ≤ x + y ≤ ( 2 n + 1 ) π ; n ∈ I Hence we get the area S = 2 π .144 ⇒ 9 π S = 8

Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesMedium2 minQB

MathematicsMediuminteger

Let $R = {x, y : x^{2} + y^{2} \leq 144$ and $sin (x + y) \geq 0}$ . And $S$ be the area of region given by $R$ , then find $S /9 π$ .

Answer:

Solution:

$x^{2} + y^{2} \leq 144$ and $sin (x + y) \geq 0 \Rightarrow 2 nπ \leq x + y \leq (2 n + 1) π; n \in I$

Hence we get the area

$S = \frac{π .144}{2} \Rightarrow \frac{S}{9 π} = 8$

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

⏱ 2mℹ️ Source: QB

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