Ex 8.1, 13 - Chapter 8 Class 12 Application of Integrals

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Ex 8.1, 13 Area of the region bounded by the curve 𝑦2=4𝑥, 𝑦-axis and the line 𝑦 = 3 is (A) 2 (B) 9﷮4﷯ (C) 9﷮3﷯ (D) 9﷮3﷯ Let AB represent the line 𝑦=3 & BOC represent the curve 𝑦﷮2﷯=4𝑥 We have to find area of shaded region Area of shaded region = Area AOB = 0﷮3﷮𝑥 𝑑𝑦﷯ We know that y2 = 4x x = 𝑦﷮2﷯﷮4﷯ Area of shaded region = 0﷮3﷮𝑥 𝑑𝑦﷯ = 0﷮3﷮ 𝑦﷮2﷯﷮4﷯ 𝑑𝑦﷯ = 1﷮4﷯ 0﷮3﷮ 𝑦﷮2﷯ 𝑑𝑦﷯ = 1﷮4﷯ 𝑦﷮3﷯﷮3﷯﷯﷮0﷮3﷯ = 1﷮4﷯ 3﷮3﷯ − 0﷮3﷯﷮3﷯﷯ = 1﷮4﷯ 27﷮3﷯﷯ = 𝟗﷮𝟒﷯ Hence, option (B) is correct