**Misc 11**

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Misc 11 Using the method of integration find the area bounded by the curve 𝑥+ 𝑦=1 [Hint: The required region is bounded by lines 𝑥+𝑦= 1, 𝑥 –𝑦=1, –𝑥+𝑦 =1 and −𝑥 −𝑦=1 ] We know that │𝑥│= 𝑥, 𝑥≥0&−𝑥, 𝑥<0 & │𝑦│= 𝑦, 𝑦≥0&−𝑦, 𝑦<0 So, we can write │𝑥│+│𝑦│=1 as 𝑥+𝑦=1 𝑓𝑜𝑟 𝑥>0 , 𝑦>0−𝑥+𝑦=1 𝑓𝑜𝑟 𝑥<0 𝑦>0 𝑥−𝑦 =1 𝑓𝑜𝑟 𝑥>0 , 𝑦<0−𝑥−𝑦=1 𝑓𝑜𝑟 𝑥<0 𝑦<0 For 𝒙+𝒚=𝟏 For −𝒙+𝒚=𝟏 Hence the figure is Since the Curve symmetrical about 𝑥 & 𝑦−𝑎𝑥𝑖𝑠 Required Area = 4 × Area AOB Area AOB Area ABO = 01𝑦 𝑑𝑥 where 𝑥+𝑦=1 𝑦=1−𝑥 Therefore, Area ABO = 01 1−𝑥 𝑑𝑥 = 𝑥− 𝑥2201 =1− 122− 0− 0222 =1− 12 = 12 Hence, Required Area = 4 × Area AOB = 4 × 12 = 2 square units

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can contact him here.