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Ex 8.1, 3 - Find area x2 = 4y, y = 2, y = 4 and y-axis - NCERT - Area bounded by curve and horizontal or vertical line

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  1. Chapter 8 Class 12 Application of Integrals
  2. Serial order wise
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Ex 8.1, 3 Find the area of the region bounded by 𝑥2= 4𝑦 , 𝑦 = 2 , 𝑦4 and the 𝑦-axis in the first quadrant. Let AB represent line 𝑦=2 CD represent line 𝑦=4 and CBOAD represent the curve 𝑥﷮2﷯=4𝑦 We have to find area of BCFE Area of BCFE = 2﷮4﷮𝑥﷯𝑑𝑥 We know that 𝑥﷮2﷯=4𝑦 Taking square root on both sides 𝑥=± ﷮4𝑦﷯‖ 𝑥=±2 ﷮𝑦﷯ Since, BCEF is in 1st Quadrant ∴ 𝑥=2 ﷮𝑦﷯ Area of BCFE = 2﷮4﷮𝑥﷯𝑑𝑥 = 2﷮4﷮2 ﷮𝑦﷯﷯𝑑𝑦 = 2 2﷮4﷮ 𝑦﷯﷮ 1﷮2﷯﷯𝑑𝑦﷯ = 2 𝑦﷮ 3﷮2﷯﷯﷮ 3﷮2﷯﷯﷯﷮2﷮4﷯ = 2 × 2﷮3﷯ 𝑦﷮ 3﷮2﷯﷯﷯﷮2﷮4﷯ = 4﷮3﷯ 4﷯﷮ 3﷮2﷯ ﷯− 2﷯﷮ 3﷮2﷯﷯﷯ = 4﷮3﷯ 4﷯﷮ 1﷮2﷯﷯﷯﷮3﷯− 2﷯﷮ 1﷮2﷯﷯﷯﷮3﷯﷯ = 4﷮3﷯ 2﷯﷮3﷯− ﷮2﷯﷯﷮3﷯﷯ = 4﷮3﷯ 8 −2 ﷮2﷯﷯ = 32 − 8 ﷮2﷯﷮3﷯ Thus , Area = 𝟑𝟐 − 𝟖 ﷮𝟐﷯﷮𝟑﷯ square units

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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