# Misc 12 - Chapter 8 Class 12 Application of Integrals

Last updated at Nov. 15, 2019 by Teachoo

Last updated at Nov. 15, 2019 by Teachoo

Transcript

Misc 12 Find the area bounded by curves {(𝑥, 𝑦) :𝑦≥ 𝑥2 and 𝑦=|𝑥|} Step 1: Drawing figure Parabola is 𝑥2=𝑦 And y = 𝑥 = 𝑥, 𝑥≥0&−𝑥, 𝑥<0 Step 2: Finding intersecting points A & B Step 3: Finding Area Required area is symmetrical about y-axis So, Required Area = 2 × Area ODBC Area ODBC Area ODBC = Area ODBE – Area OCBE Area ODBE Area ODBE = 01𝑦 𝑑𝑥 y → Equation of line y = x Therefore, Area ODBE = 01𝑥 𝑑𝑥 = 𝑥2201 = 12 2− 022 = 12 Area OCBE Area OCBE = 01𝑦 𝑑𝑥 y → Equation of parabola y = x2 Therefore, Area OCBE = 01 𝑥2 𝑑𝑥 = 𝑥3301 = 133− 033 = 13 Hence, Area ODBC = Area ODBE – Area OCBE = 12− 13 = 16 Also, Required Area = 2 × Area ODBC = 2 × 16 = 13

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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.