# Example 9 - Chapter 8 Class 12 Application of Integrals (Term 2)

Last updated at Nov. 15, 2019 by Teachoo

Last updated at Nov. 15, 2019 by Teachoo

Transcript

Example 9 Using integration find the area of region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1) Area of ∆ formed by point 1 , 0 , 2 ,2 & 3 , 1 Step 1: Draw the figure Area ABD Area ABD= 12𝑦 𝑑𝑥 𝑦→ equation of line AB Equation of line between A(1, 0) & B(2, 2) is 𝑦 − 0𝑥 − 1= 2 − 02 − 1 𝑦𝑥 − 1= 21 y = 2(x – 1) y = 2x – 2 Area ABD = 12𝑦 𝑑𝑥 = 122 𝑥−1 𝑑𝑥 = 2 𝑥22−𝑥12 =2 222−2− 122−1 =2 2−2− 12+1 =2 12 = 1 Area BDEC Area BDEC = 23𝑦 𝑑𝑥 𝑦→ equation of line BC Equation of line between B(2, 2) & C(3, 1) is 𝑦 − 2𝑥 − 2= 1 − 23 − 2 𝑦 − 2𝑥 − 2= −11 y – 2 = –1(x – 2) y – 2 = –x + 2 y = 4 – x Area BDEC = 23𝑦 𝑑𝑥 = 23 4−𝑥 𝑑𝑥 =4 23𝑑𝑥− 23𝑥𝑑𝑥 =4 𝑥23− 𝑥2223 =4 3−2− 12 32− 22 =4 ×1− 12 9−4 =4− 12 ×5 = 4− 52 = 8 − 52 = 32 Area ACE Area ACE= 13𝑦 𝑑𝑥 𝑦→ equation of line AC Equation of line between A(1, 0) & C(3, 1) is 𝑦 − 0𝑥 − 1= 1 − 03 − 1 𝑦𝑥 − 1= 12 y = 12 (x – 1) Area ACE = 13𝑦 𝑑𝑥 = 13 12 𝑥−1 𝑑𝑥 = 12 13 𝑥−1 𝑑𝑥 = 12 𝑥22−𝑥13 = 12 322−3− 122−1 = 12 92−3− 12+1 = 12 42 =1 Hence Area Required = Area ABD + Area BDEC – Area ACE = 1 + 32−1 = 32

Examples

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Example 2 Important

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Example 5 Important

Example 6 Important Deleted for CBSE Board 2022 Exams

Example 7 Important Deleted for CBSE Board 2022 Exams

Example 8 Important Deleted for CBSE Board 2022 Exams

Example 9 Deleted for CBSE Board 2022 Exams You are here

Example 10 Important Deleted for CBSE Board 2022 Exams

Example 11

Example 12

Example 13 Important

Example 14 Important Deleted for CBSE Board 2022 Exams

Example 15 Important

Chapter 8 Class 12 Application of Integrals (Term 2)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.