# Misc 17

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 17 The area bounded by the curve 𝑦 = 𝑥 |𝑥| , 𝑥−𝑎𝑥𝑖𝑠 and the ordinates 𝑥 = – 1 and 𝑥=1 is given by (A) 0 (B) 13 (C) 23 (D) 43 [Hint : 𝑦=𝑥2 if 𝑥 > 0 𝑎𝑛𝑑 𝑦 =−𝑥2 if 𝑥 < 0] We know that 𝑥= 𝑥, 𝑥≥0&−𝑥, 𝑥<0 Therefore, y = x 𝑥= 𝑥𝑥, 𝑥≥0&𝑥(−𝑥), 𝑥<0 y = 𝑥2 𝑥≥0&− 𝑥2, 𝑥<0 Area Required = Area ABO + Area BCO Area ABO Area ABO = −10𝑦 𝑑𝑥 Here, 𝑦= −𝑥2 Therefore, Area ABO = −10 −𝑥2 𝑑𝑥 =− 𝑥33−10 =− 033− −133 = −13 Since Area is always positive, Area ABO = 13 Area DCO Area DCO = 01𝑦 𝑑𝑥 Here, 𝑦= 𝑥2 Therefore, Area DCO = 01 𝑥2 𝑑𝑥 = 𝑥3301 = 13 13− 03 = 13 1−0 = 13 ∴ Required Area = Area ABO + Area DCO = 13+ 13 = 23 So, Option C is Correct

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.