Ex 8.2

Chapter 8 Class 12 Application of Integrals
Serial order wise

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Ex 8.2 , 3 Find the area of the region bounded by the curves π¦=π₯2+2, π¦=π₯, π₯=0 and π₯=3 Here, π¦=π₯2+2 π¦β2=π₯^2 π₯^2=(π¦β2) So, it is a parabola And, π₯=π¦ 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¦β2) 3^2=(π¦β2) 9 = π¦β2 π¦=11 Hence, B = (3 , 11) Point C Point C is the intersection of x = 3 and x = y Putting π₯=3 in π₯=π¦ 3=π¦ i.e. π¦=3 Hence C = (3 , 3) Finding Area Area required = Area ABDO β Area OCD Area ABDO Area ABDO = β«_0^3βγπ¦ ππ₯γ π¦β Equation of parabola AB π¦=π₯^2+2 β΄ Area ABDO = β«_0^3βγπ¦ ππ₯γ = β«_0^3βγ(π₯^2+2) ππ₯γ = [π₯^3/3+2π₯]_0^3 = [3^3/3+2 Γ3β0^3/3] = 9+6 = 15 Area OCD Area OCD = β«_0^3βγπ¦ ππ₯γ π¦β equation of line π¦=π₯ β΄ Area OCD = β«_0^3βγπ¦ ππ₯γ = β«_0^3βγπ₯ ππ₯γ = [π₯^2/2]_0^3 =[3^2/2β0^2/2] = 9/2 Area required = Area ABDO β Area OCD = 15 β 9/2 = ππ/π square units