Find the area of the region bounded by the parabola ๐‘ฆ 2 = 8๐‘ฅ and the line ๐‘ฅ = 2.

 

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Note : This is similar to Ex 8.1, 11 of NCERT – Chapter 8 Class 12 Applications of Integration

Check the answer here https:// www.teachoo.com /3335/730/Ex-8.1--11---Find-area-bounded-by-y2--4x-and-line-x--3/category/Ex-8.1/

  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 24 Find the area of the region bounded by the parabola ๐‘ฆ2 = 8๐‘ฅ and the line ๐‘ฅ = 2. Let AB represents the line ๐‘ฅ=2 and AOB represent the curve ๐‘ฆ^2=8๐‘ฅ Area of AOBC = 2 ร— [Area of AOC] = 2 ร— โˆซ_๐ŸŽ^๐Ÿโ–’ใ€–๐’š.๐’…๐’™ใ€— We know that ๐‘ฆ^2=8๐‘ฅ ๐‘ฆ=ยฑโˆš8๐‘ฅ ๐’š=ยฑ๐Ÿโˆš๐Ÿ๐’™ As AOC is in 1st Quadrant โˆด ๐‘ฆ=2โˆš2 โˆš๐‘ฅ โˆด Area of AOBC = 2 ร— โˆซ_0^2โ–’ใ€–๐‘ฆ.๐‘‘๐‘ฅใ€— = 2 โˆซ_0^2โ–’ใ€–2โˆš2 โˆš๐‘ฅ ๐‘‘๐‘ฅใ€— = 4โˆš2 โˆซ_0^2โ–’ใ€–โˆš๐‘ฅ ๐‘‘๐‘ฅใ€— = 4โˆš2 โˆซ_0^2โ–’ใ€–(๐‘ฅ)^(1/2) ๐‘‘๐‘ฅใ€— = 4โˆš2 [๐‘ฅ^(1/2+1)/(1/2+1)]_0^2 =4โˆš2 ร— 2/3 [๐‘ฅ^(3/2) ]_0^2 = (8โˆš2)/3 [(2)^(3/2)โˆ’0] = (8โˆš2)/3 [(2)^(3/2)โˆ’0] =(8โˆš2)/3 [(โˆš2)^3 ] =(8โˆš2)/3 [ โˆš2 ร— โˆš2 ร— โˆš2 ] = 8/3 [ 2 ร— 2] = ๐Ÿ‘๐Ÿ/๐Ÿ‘ square units โˆด Required Area = ๐Ÿ‘๐Ÿ/๐Ÿ‘ square units

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.