Question 24 - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

Find the area of the region bounded by the parabola 𝑦 ² = 8𝑥 and the line 𝑥 = 2.

Find area of the region bounded by parabola y^2 = 8x and line x = 2

Question 24 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

Question 24 - CBSE Class 12 Sample Paper for 2021 Boards - Part 3

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/

Transcript

Question 24 Find the area of the region bounded by the parabola 𝑦2 = 8𝑥 and the line 𝑥 = 2. Let AB represents the line 𝑥=2 and AOB represent the curve 𝑦^2=8𝑥 Area of AOBC = 2 × [Area of AOC] = 2 × ∫_𝟎^𝟐▒〖𝒚.𝒅𝒙〗 We know that 𝑦^2=8𝑥 𝑦=±√8𝑥 𝒚=±𝟐√𝟐𝒙 As AOC is in 1st Quadrant ∴ 𝑦=2√2 √𝑥 ∴ Area of AOBC = 2 × ∫_0^2▒〖𝑦.𝑑𝑥〗 = 2 ∫_0^2▒〖2√2 √𝑥 𝑑𝑥〗 = 4√2 ∫_0^2▒〖√𝑥 𝑑𝑥〗 = 4√2 ∫_0^2▒〖(𝑥)^(1/2) 𝑑𝑥〗 = 4√2 [𝑥^(1/2+1)/(1/2+1)]_0^2 =4√2 × 2/3 [𝑥^(3/2) ]_0^2 = (8√2)/3 [(2)^(3/2)−0] = (8√2)/3 [(2)^(3/2)−0] =(8√2)/3 [(√2)^3 ] =(8√2)/3 [ √2 × √2 × √2 ] = 8/3 [ 2 × 2] = 𝟑𝟐/𝟑 square units ∴ Required Area = 𝟑𝟐/𝟑 square units

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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