Example 3 - Find area bounded by y = x2 and line y = 4 - Examples

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  1. Chapter 8 Class 12 Application of Integrals
  2. Serial order wise
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Example 3 Find the area of the region bounded by the curve 𝑦=𝑥2 and the line 𝑦=4 Given that y = 4 Let Line AB represent y = 4 Also, y = x2 x2 = y Let AOB represent x2 = y We have to find area of AOBA Area of AOBA = 2 × Area BONB = 2 0﷮4﷮𝑥 𝑑𝑦﷯ We know that 𝑥﷮2﷯= 𝑦 𝑥 = ± ﷮𝑦﷯ Since BONB is in first quadrant we use x = + ﷮𝑦﷯ Area of AOBA = 2 0﷮4﷮𝑥 𝑑𝑦﷯ = 2 0﷮4﷮ ﷮𝑦﷯ 𝑑𝑦﷯ = 2 0﷮4﷮ 𝑦﷯﷮ 1﷮2﷯﷯﷮ ﷯𝑜𝑦﷯ = 2 𝑦﷮ 1﷮2﷯ + 1﷯﷮ 1﷮2﷯ + 1﷯﷯﷮0﷮4﷯ = 2 𝑦﷮ 1 + 2﷮2﷯ ﷯﷮ 1 + 2﷮2﷯﷯﷯﷮0﷮4﷯ = 2 𝑦﷮ 3﷮2﷯ ﷯﷮ 3﷮2﷯﷯﷯﷮0﷮4﷯ = 2.2﷮3﷯ 𝑦﷮ 3﷮2﷯ ﷯﷯﷮0﷮4﷯ = 4﷮3﷯ [(4)﷮ 3﷮2﷯ ﷯−0] = 4﷮3﷯ ( 2﷮2﷯)﷮ 3﷮2﷯ ﷯﷯ = 4﷮3﷯ × 23 = 𝟑𝟐﷮𝟑﷯

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