Misc 16 - Chapter 8 Class 12 Application of Integrals

Transcript

Misc 16 Area bounded by the curve 𝑦=𝑥3, the 𝑥-axis and the ordinates 𝑥 = – 2 and 𝑥 = 1 is (A) – 9 (B) −15﷮4﷯ (C) 𝟏𝟓﷮𝟒﷯ (D) 𝟏𝟕﷮𝟒﷯ Area Required = Area ABO + Area BCO Area ABO Area ABO = −2﷮0﷮𝑦 𝑑𝑥﷯ Here, 𝑦= 𝑥﷮3﷯ Therefore, Area ABO = −2﷮0﷮ 𝑥﷮3﷯ 𝑑𝑥﷯ = 𝑥﷮4﷯﷮4﷯﷯﷮−2﷮0﷯ = 1﷮4﷯ 0− −2﷯﷮4﷯﷯ = 1﷮4﷯ × −16﷯ =−4 Since Area is always positive, Area ABO = 4 Area DCO Area DCO = 0﷮1﷮𝑦 𝑑𝑥﷯ = 0﷮1﷮ 𝑥﷮3﷯ 𝑑𝑥﷯ = 𝑥﷮4﷯﷮4﷯﷯﷮0﷮1﷯ = 1﷮4﷯ 1﷮3﷯− 0﷮3﷯﷯ = 1﷮4﷯ ∴ Area Required = Area ABO + Area DCO =4+ 1﷮4﷯ = 17﷮4﷯ ∴ D is the Correct Option