Question

using green's theorem to find area of the region in the first quadrant bounded by the curves y = x y = 1/x and y = x/4

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Answer 1

Step-by-step explanation:

Given using green's theorem to find area of the region in the first quadrant bounded by the curves y = x y = 1/x and y = x/4

• Applying Green’s theorem we have,
• Area = 1/2 P ∫ (x dy – y dx)
•           = 1/2 (P1 ∫ + P2 ∫ + P3 ∫)
•            = 1/2 [P1 ∫ (x dy – y dx) + P2∫ (x dy – y dx) + P3 ∫(x dy – y dx)]
•      So P1 is y = x/4, P2 is y = 1/x and P 3 is y = x
• Therefore P1 ∫(x dy – y dx)
•                  = 0 to 2 ∫ (x/4 – x/4) dx = 0
•  Also    ∫ P2 (x dy – y dx)
•                                     = 1 ∫- 1/x dx – 1/x dx
•                                      = - 2  1 ∫1/x dx
•                                    = 2 log 2  
•  Similarly ∫ P3 x dy – y dx  
•                                        = 1 to 0 ∫(x dx – x dx )
•                                         = 0
• Therefore P ∫ (x dy – y dx)
•                                           = 1/2 (0 + 2 log 2 + 0)
•                                           = log 2

Reference link will be

https://brainly.in/question/19187598

https://brainly.in/question/5952668