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CBSE Class 12 Sample Paper for 2021 Boards

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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 Oct. 27, 2020 by

Find the area of the region bounded by the parabola 𝑦 2 = 8π‘₯ and the line π‘₯ = 2.

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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

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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/

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Transcript

Question 24 Find the area of the region bounded by the parabola 𝑦2 = 8π‘₯ and the line π‘₯ = 2. Let AB represents the line π‘₯=2 and AOB represent the curve 𝑦^2=8π‘₯ Area of AOBC = 2 Γ— [Area of AOC] = 2 Γ— ∫_𝟎^πŸβ–’γ€–π’š.𝒅𝒙〗 We know that 𝑦^2=8π‘₯ 𝑦=±√8π‘₯ π’š=Β±πŸβˆšπŸπ’™ As AOC is in 1st Quadrant ∴ 𝑦=2√2 √π‘₯ ∴ Area of AOBC = 2 Γ— ∫_0^2▒〖𝑦.𝑑π‘₯γ€— = 2 ∫_0^2β–’γ€–2√2 √π‘₯ 𝑑π‘₯γ€— = 4√2 ∫_0^2β–’γ€–βˆšπ‘₯ 𝑑π‘₯γ€— = 4√2 ∫_0^2β–’γ€–(π‘₯)^(1/2) 𝑑π‘₯γ€— = 4√2 [π‘₯^(1/2+1)/(1/2+1)]_0^2 =4√2 Γ— 2/3 [π‘₯^(3/2) ]_0^2 = (8√2)/3 [(2)^(3/2)βˆ’0] = (8√2)/3 [(2)^(3/2)βˆ’0] =(8√2)/3 [(√2)^3 ] =(8√2)/3 [ √2 Γ— √2 Γ— √2 ] = 8/3 [ 2 Γ— 2] = πŸ‘πŸ/πŸ‘ square units ∴ Required Area = πŸ‘πŸ/πŸ‘ square units

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