Let R denote the circular region in the x y -plane bounded by the circle x^2+y^2=36 . The lines x=4 and y=3 divide R into four regions R_i, i=1,2,3 , 4 . If |R_i | denotes the area of the region R_i and if | R ₁ | | R ₂ | | R ₃ | | R ₄ |

Question

Let R denote the circular region in the x y -plane bounded by the circle x^2+y^2=36 . The lines x=4 and y=3 divide R into four regions R_i, i=1,2,3 , 4 . If |R_i | denotes the area of the region R_i and if | R ₁ |> | R ₂ |> | R ₃ |> | R ₄ | , determine | R ₁ |- | R ₂ |- | R ₃ |+ | R ₄ | . [Here | | denotes the area of the region in the plane.]

Quantrex Academy · Accepted Answer

Correct answer: 48

R₁= _ -2 5 ^3 36-y^2 d y= 1 2 y 36-y^2 + 1 2 (36) ⁻¹ y 6 Similarly for using integration. we can find gathered R ₁+ R ₄= 1 2 (6)^2+2(3)(4) Remaining circle area = R ₂+ R ₃= 1 2 (6)^2-2(3)(4) gathered Hence, R₁+R₄- (R₂+R₃ )=24+24=48

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