Misc 2 - Find area between y = x, y = x2 - Class 12 NCERT - Area between curve and line

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

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Question 1 Find the area between the curves 𝑦 = 𝑥 and 𝑦 = 𝑥2 Step 1: Drawing figure Parabola is y = x2 Also, 𝑦=𝑥 passes through (0, 0) & (1, 1) Point (1, 1) lies in parabola y2 = x Hence, intersecting point A = (1, 1) Area required Area required = Area OAD – Area OBAD Area OAD Area OAD = 0﷮1﷮𝑦 𝑑𝑥﷯ y → Equation of line y = x Therefore, Area OAD = 0﷮1﷮𝑥 𝑑𝑥﷯ = 0﷮1﷮𝑥 𝑑𝑥﷯ = 𝑥﷮2﷯﷮2﷯﷯﷮0﷮1﷯ = 1﷮2﷯ 1﷮2﷯− 0﷮2﷯﷯ = 1﷮2﷯ Area OBAD Area OBAD = 0﷮1﷮𝑦 𝑑𝑥﷯ y → Equation of parabola y = x2 Therefore, Area OBAD = 0﷮1﷮ 𝑥﷮2﷯ 𝑑𝑥﷯ = 𝑥﷮3﷯﷮3﷯﷯﷮0﷮1﷯ = 1﷮3﷯ 1﷮3﷯− 0﷮3﷯﷯ = 1﷮3﷯ Area required = Area OAD – Area OBAD = 1﷮2﷯ – 1﷮3﷯ = 1﷮6﷯

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo