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Misc 10 - Find area enclosed by parabola  x2 = y, t = x + 2 - Miscellaneous

Misc 10 - Chapter 8 Class 12 Application of Integrals - Part 2
Misc 10 - Chapter 8 Class 12 Application of Integrals - Part 3
Misc 10 - Chapter 8 Class 12 Application of Integrals - Part 4
Misc 10 - Chapter 8 Class 12 Application of Integrals - Part 5

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Misc 10 Find the area of the region enclosed by the parabola 𝑥﷮2﷯=𝑦, the line 𝑦=𝑥+2 and the 𝑥−axis Step 1: Draw the Figure Parabola is 𝑥﷮2﷯=𝑦 Also, 𝑦=𝑥+2 is a straight line Step 2: Finding point of intersection A & B Equation of line is 𝑦=𝑥+2 Putting value of y in equation of parabola 𝑥﷮2﷯=𝑦 𝑥﷮2﷯=𝑥+2 𝑥﷮2﷯−𝑥−2=0 𝑥﷮2﷯−2𝑥+𝑥−2=0 𝑥(x−2) +1(𝑥−2)=0 (𝑥+1)(𝑥−2)=0 So, x = –1, x = 2 Required Area Area required = Area ADOEB – Area ADOEBC Area ADOEB Area ADOEB = −1﷮2﷮𝑦 𝑑𝑥﷯ y → Equation of line y = x + 2 Therefore, Area ADOEB = −1﷮2﷮ 𝑥+2﷯ 𝑑𝑥﷯ = 𝑥﷮2﷯﷮2﷯+2𝑥﷯﷮−1﷮2﷯ = 2﷯﷮2﷯﷮2﷯+2 2﷯− −1﷯﷮2﷯﷮2﷯+2 −1﷯﷯ = 2+ 4 – 1﷮2﷯ + 2 = 15﷮2﷯ Area ADOEBC Area ADOEBC = −1﷮2﷮𝑦 𝑑𝑥﷯ y → Equation of parabola 𝑥﷮2﷯=𝑦 𝑦= 𝑥﷮2﷯ Therefore, Area ADOEBC = −1﷮2﷮ 𝑥﷮2﷯ 𝑑𝑥﷯ = 𝑥﷮3﷯﷮3﷯﷯﷮−1﷮2﷯ = 1﷮3﷯ 2﷯﷮3﷯− −1﷯﷮3﷯﷯ = 9﷮3﷯ = 3 Area required = Area ADOEB – Area ADOEBC = 15﷮2﷯ – 3 = 9﷮2﷯

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.