Misc 16 - Area bounded by y = x3, the x-axis, x = -2, 1 - Miscellaneou

Misc 16 - Chapter 8 Class 12 Application of Integrals - Part 2
Misc 16 - Chapter 8 Class 12 Application of Integrals - Part 3

  1. Chapter 8 Class 12 Application of Integrals (Term 2)
  2. Serial order wise

Transcript

Misc 16 Area bounded by the curve 𝑦=π‘₯3, the π‘₯-axis and the ordinates π‘₯ = – 2 and π‘₯ = 1 is (A) – 9 (B) (βˆ’15)/4 (C) 15/4 (D) 17/4 Area Required = Area ABO + Area DCO Area ABO Area ABO =∫_(βˆ’2)^0▒〖𝑦 𝑑π‘₯γ€— Here, 𝑦=π‘₯^3 Therefore, Area ABO =∫_(βˆ’2)^0β–’γ€–π‘₯^3 𝑑π‘₯γ€— γ€–=[π‘₯^4/4]γ€—_(βˆ’2)^0 =1/4 [0βˆ’(βˆ’2)^4 ] =1/4 Γ— (βˆ’16) =βˆ’4 Since Area is always positive, Area ABO = 4 Area DCO Area DCO = ∫_0^1▒〖𝑦 𝑑π‘₯γ€— =∫_0^1β–’γ€–π‘₯^3 𝑑π‘₯γ€— =[π‘₯^4/4]_0^1 =1/4 [1^3βˆ’0^3 ] =1/4 ∴ Area Required = Area ABO + Area DCO =4+1/4 =17/4 ∴ D is the Correct Option

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.