Check sibling questions

Ex 8.2, 3 - Find area bounded by: y = x2 + 2, y = x, x=0,3

Ex 8.2, 3 - Chapter 8 Class 12 Application of Integrals - Part 2
Ex 8.2, 3 - Chapter 8 Class 12 Application of Integrals - Part 3
Ex 8.2, 3 - Chapter 8 Class 12 Application of Integrals - Part 4
Ex 8.2, 3 - Chapter 8 Class 12 Application of Integrals - Part 5

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Transcript

Ex 8.2 , 3 Find the area of the region bounded by the curves 𝑦=π‘₯2+2, 𝑦=π‘₯, π‘₯=0 and π‘₯=3 Here, 𝑦=π‘₯2+2 π‘¦βˆ’2=π‘₯^2 π‘₯^2=(π‘¦βˆ’2) So, it is a parabola And, π‘₯=𝑦 is a line x = 3 is a line x = 0 is the y-axis Finding point of intersection B & C Point B Point B is intersection of x = 3 and parabola Putting π‘₯=3 in π‘₯^2=(π‘¦βˆ’2) 3^2=(π‘¦βˆ’2) 9 = π‘¦βˆ’2 𝑦=11 Hence, B = (3 , 11) Point C Point C is the intersection of x = 3 and x = y Putting π‘₯=3 in π‘₯=𝑦 3=𝑦 i.e. 𝑦=3 Hence C = (3 , 3) Finding Area Area required = Area ABDO – Area OCD Area ABDO Area ABDO = ∫_0^3▒〖𝑦 𝑑π‘₯γ€— 𝑦→ Equation of parabola AB 𝑦=π‘₯^2+2 ∴ Area ABDO = ∫_0^3▒〖𝑦 𝑑π‘₯γ€— = ∫_0^3β–’γ€–(π‘₯^2+2) 𝑑π‘₯γ€— = [π‘₯^3/3+2π‘₯]_0^3 = [3^3/3+2 Γ—3βˆ’0^3/3] = 9+6 = 15 Area OCD Area OCD = ∫_0^3▒〖𝑦 𝑑π‘₯γ€— 𝑦→ equation of line 𝑦=π‘₯ ∴ Area OCD = ∫_0^3▒〖𝑦 𝑑π‘₯γ€— = ∫_0^3β–’γ€–π‘₯ 𝑑π‘₯γ€— = [π‘₯^2/2]_0^3 =[3^2/2βˆ’0^2/2] = 9/2 Area required = Area ABDO – Area OCD = 15 – 9/2 = 𝟐𝟏/𝟐 square units

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.