Question 24 Find the area of the region bounded by the parabola ๐ฆ2 = 8๐ฅ and the line ๐ฅ = 2.
Let
AB represents the line ๐ฅ=2
and AOB represent the curve ๐ฆ^2=8๐ฅ
Area of AOBC = 2 ร [Area of AOC]
= 2 ร โซ_๐^๐โใ๐.๐ ๐ใ
We know that
๐ฆ^2=8๐ฅ
๐ฆ=ยฑโ8๐ฅ
๐=ยฑ๐โ๐๐
As AOC is in 1st Quadrant
โด ๐ฆ=2โ2 โ๐ฅ
โด Area of AOBC = 2 ร โซ_0^2โใ๐ฆ.๐๐ฅใ
= 2 โซ_0^2โใ2โ2 โ๐ฅ ๐๐ฅใ
= 4โ2 โซ_0^2โใโ๐ฅ ๐๐ฅใ
= 4โ2 โซ_0^2โใ(๐ฅ)^(1/2) ๐๐ฅใ
= 4โ2 [๐ฅ^(1/2+1)/(1/2+1)]_0^2
=4โ2 ร 2/3 [๐ฅ^(3/2) ]_0^2
= (8โ2)/3 [(2)^(3/2)โ0]
= (8โ2)/3 [(2)^(3/2)โ0]
=(8โ2)/3 [(โ2)^3 ]
=(8โ2)/3 [ โ2 ร โ2 ร โ2 ]
= 8/3 [ 2 ร 2]
= ๐๐/๐ square units
โด Required Area = ๐๐/๐ square units

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.