Example 11 - Find area of parabola y2=4ax bounded by latus - Examples

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  1. Chapter 8 Class 12 Application of Integrals
  2. Serial order wise
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Example 11 Find the area of the parabola 𝑦2=4𝑎𝑥 bounded by its latus rectum For Parabola 𝑦﷮2﷯=4 𝑎𝑥 Latus rectum is line 𝑥=𝑎 Area required = Area OLSL’ =2 × Area OSL = 2 × 0﷮𝑎﷮𝑦 𝑑𝑥﷯ 𝑦 → Parabola equation 𝑦﷮2﷯=4 𝑎𝑥 𝑦=± ﷮4 𝑎𝑥﷯ Since OSL is in 1st quadrant 𝑦= ﷮4 𝑎𝑥﷯ Area required = 2 × 0﷮𝑎﷮𝑦 𝑑𝑥﷯ = 2 0﷮𝑎﷮ ﷮4 𝑎𝑥﷯ 𝑑𝑥﷯ = 2 0﷮𝑎﷮ ﷮4 𝑎﷯ ﷮𝑥﷯ 𝑑𝑥﷯ = 2 ﷮4 𝑎﷯ 0﷮𝑎﷮ ﷮𝑥﷯ 𝑑𝑥﷯ = 4 ﷮ 𝑎﷯ 0﷮𝑎﷮ ﷮𝑥﷯ 𝑑𝑥﷯ = 4 ﷮ 𝑎﷯ 𝑥﷮ 3﷮2﷯﷯﷮ 3﷮2﷯﷯﷯﷮0﷮𝑎﷯ = 4 ﷮ 𝑎﷯ × 2﷮3﷯ 𝑥﷮ 3﷮2﷯﷯﷯﷮0﷮𝑎﷯ = 8﷮3﷯ ﷮ 𝑎﷯ 𝑎﷮ 3﷮2﷯﷯−0﷯ = 8﷮3﷯ ﷮ 𝑎﷯ 𝑎﷮ 3﷮2﷯﷯ = 8﷮3﷯ 𝑎﷮ 1﷮2﷯﷯ 𝑎﷮ 3﷮2﷯﷯ = 8﷮3﷯ 𝑎﷮ 1﷮2﷯ + 3﷮2﷯﷯ = 8﷮3﷯ 𝑎﷮ 4﷮2﷯ ﷯ = 𝟖﷮𝟑﷯ 𝒂﷮𝟐﷯

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