Ex 8.1, 11 - Find area bounded by y2 = 4x and line x = 3 - 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, 11 Find the area of the region bounded by the curve 𝑦2=4𝑥 and the line 𝑥=3 . Let AB represents the line 𝑥=3 and AOB represent the curve 𝑦﷮2﷯=4𝑥 Area of AOBC = 2 × [Area of AOC] = 2 × 0﷮3﷮𝑦.𝑑𝑥﷯ We know that 𝑦﷮2﷯=4𝑥 𝑦=± ﷮4𝑥﷯ 𝑦=±2 ﷮𝑥﷯ As AOC is in 1st Quadrant ∴ 𝑦=2 ﷮𝑥﷯ ∴ Area of AOBC = 2 × 0﷮3﷮𝑦.𝑑𝑥﷯ = 2 0﷮3﷮2 ﷮𝑥﷯𝑑𝑥﷯ = 4 0﷮3﷮ ﷮𝑥﷯𝑑𝑥﷯ = 4 0﷮3﷮ 𝑥﷯﷮ 1﷮2﷯﷯𝑑𝑥﷯ = 4 𝑥﷮ 1﷮2﷯+1﷯﷮ 1﷮2﷯+1﷯﷯﷮0﷮3﷯ = 4.2﷮3﷯ 𝑥﷮ 3﷮2﷯﷯﷯﷮0﷮3﷯ = 8﷮3﷯ 3﷯﷮ 3﷮2﷯﷯−0﷯ = 8﷮3﷯ 3﷯﷮ 3﷮2﷯﷯−0﷯ = 8﷮3﷯ ﷮3﷯﷯﷮3﷯﷯ = 8﷮3﷯ ﷮3﷯ × ﷮3﷯ × ﷮3﷯ ﷯ = 8﷮3﷯ 3 ﷮3﷯ ﷯ = 8 ﷮3﷯ ∴ Required Area = 𝟖 ﷮𝟑﷯ square units

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