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Misc 15 - Find area {(x, y): y2 < 4x, 4x2 + 4y2 < 9} - Area between curve and curve

Misc 15 - Chapter 8 Class 12 Application of Integrals - Part 2
Misc 15 - Chapter 8 Class 12 Application of Integrals - Part 3
Misc 15 - Chapter 8 Class 12 Application of Integrals - Part 4
Misc 15 - Chapter 8 Class 12 Application of Integrals - Part 5
Misc 15 - Chapter 8 Class 12 Application of Integrals - Part 6
Misc 15 - Chapter 8 Class 12 Application of Integrals - Part 7
Misc 15 - Chapter 8 Class 12 Application of Integrals - Part 8
Misc 15 - Chapter 8 Class 12 Application of Integrals - Part 9
Misc 15 - Chapter 8 Class 12 Application of Integrals - Part 10

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Transcript

Misc 15 Find the area of the region { , : 2 4 , 4 2+ 4 2 9} Drawing figures Now, our figure will be Circle is 4 2+ 4 2 9 2+ 2 9 4 2+ 2 3 2 2 Radius of circle = 3 2 So, Point C ( 3 2 , 0) Finding point of intersection A & B Solving 2 =4 (1) & 4 2+ 4 2= 9 (2) Putting (1) in (2) 4 2+ 4 2= 9 4 2+ 4 4 =9 4 2+16 9=0 4 2+18 2 9=0 2 (2 +9) 1(2 +9)=0 2 1 2 +9 =0 So, = 1 2 & = 9 2 Area OAC Area OAC = Area ACD + Area OAD Area ACD Area ACD = 1 2 3 2 Equation of circle 2 + 2 = 9 4 2 = 9 4 2 = 9 4 2 Therefore Area ACD = 1 2 3 2 9 4 2 = 1 2 3 2 3 2 2 2 = 2 3 2 2 2 + 3 2 2 2 sin 1 3 2 1 2 3 2 = 2 9 4 2 + 9 8 sin 1 2 3 1 2 3 2 = 3 2 2 9 4 3 2 2 + 9 8 sin 1 2 3 2 3 1 2 2 9 4 1 2 2 + 9 8 sin 1 2 1 2 3 = 3 4 9 4 9 4 + 9 8 sin 1 1 1 4 9 4 1 4 + 9 8 sin 1 1 3 = 9 8 sin 1 1 2 4 9 8 sin 1 1 3 = 9 16 2 4 9 8 sin 1 1 3 Area OAD Area OAD = 0 1 2 Equation of parabola 2 =4 = 4 Therefore Area OAD = 0 1 2 4 =2 0 1 2 =2 0 1 2 1 2 =2 3 2 3 2 0 1 2 = 4 3 [ 3 2 ] 0 1 2 = 4 3 1 2 3 2 0 3 2 = 4 3 1 2 2 = 4 3 1 2 2 2 2 = 2 3 Area OAC = Area ACD + Area OAD = 9 16 2 4 9 8 sin 1 1 3 + 2 3 = 9 16 9 8 sin 1 1 3 + 2 12 Required Area = 2 Area OAC = 2 9 16 9 8 sin 1 1 3 + 2 12 = 9 8 9 4 sin 1 1 3 + 2 6 = 9 8 9 4 sin 1 1 3 + 2 6 2 2 = 9 8 9 4 sin 1 1 3 + 2 6 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.