# Example 6 - Chapter 8 Class 12 Application of Integrals

Last updated at Nov. 15, 2019 by Teachoo

Last updated at Nov. 15, 2019 by Teachoo

Transcript

Example 6 Find the area of the region bounded by the two parabolas 𝑦=𝑥2 and 𝑦2 = 𝑥 Area of region between two parabola 𝑦=𝑥2 and 𝑦2=𝑥 Step 1: Drawing figure Area required = Area OABC Step 2: Finding Point of intersection B Solving 𝑦2 = 𝑥 𝑥2 =𝑦 Put (2) in (1) 𝑦2 = 𝑥 𝑥22=𝑥 𝑥4−𝑥=0 𝑥 𝑥3−1=0 Finding y – coordinate Since point B lies in 1st quadrant So, co-ordinates of B is 1 , 1 Step 3: Finding Area Area OABC = Area OABD – Area OCBD = 01 𝑦1 𝑑𝑥 – 01 𝑦2 𝑑𝑥 Area Required = 01 𝑦1 𝑑𝑥 – 01 𝑦2 𝑑𝑥 = 01 𝑥 𝑑𝑥− 01 𝑥2 𝑑𝑥 = 01 𝑥 12 𝑑𝑥− 01 𝑥2 𝑑𝑥 = 𝑥 12+1 12+101− 𝑥2+12+101 = 𝑥 32 3201− 𝑥3301 = 23 1 32− 0 32− 13 13− 03 = 23 1−0− 13 1−0 = 13 Hence, Area required = 𝟏𝟑 square units

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.