# Example 1 - Chapter 8 Class 12 Application of Integrals

Last updated at Dec. 12, 2019 by Teachoo

Last updated at Dec. 12, 2019 by Teachoo

Transcript

Example 1 Find the area enclosed by the circle ๐ฅ2 + ๐ฆ2 = ๐2 Drawing circle ๐ฅ^2 + ๐ฆ^2= ๐^2 Center = (0, 0) Radius = ๐ Hence OA = OB = Radius = ๐ A = (๐, 0) B = (0, ๐) Since Circle is symmetric about x-axis and y-axis Area of circle = 4 ร Area of Region OBAO = 4 ร โซ1_0^๐โใ๐ฆ ๐๐ฅใ We know that ๐ฅ^2 + ๐ฆ^2 = ๐^2 ๐ฆ^2 = ๐^2โ ๐ฅ^2 y = ยฑโ(๐^2โ๐ฅ^2 ) Since AOBA lies in 1st Quadrant, Value of y is positive y = โ(๐^2โ๐ฅ^2 ) Now, Area of circle = 4 ร โซ1_0^๐โใโ(๐^2โ๐ฅ^2 ) ๐๐ฅใ Using: โ(๐^2โ๐ฅ^2 )dx = 1/2 โ(๐^2โ๐ฅ^2 ) + ๐^2/2 ใ"sin" ใ^(โ1) ๐ฅ/๐ + c = 4[๐ฅ/2 โ(๐^2โ๐ฅ^2 )+๐^2/2 ใ"sin" ใ^(โ1) ๐ฅ/๐]_0^๐ = 4[(๐/2 โ(๐^2โ๐^2 )+๐^2/2 ใ"sin" ใ^(โ1) ๐/๐)โ(0/2 โ(๐^2โ0)+0^2/2 ใ"sin" ใ^(โ1) (0))] = 4[0+๐^2/2 ใ"sin" ใ^(โ1) (1)โ0โ0] = 4 ร ๐^2/2 ใ"sin" ใ^(โ1) (1) = 4 ร ๐^2/2ร ๐/2 = ๐ ๐^๐

Examples

Example 1
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Example 2 Important

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Example 5 Important

Example 6 Important Deleted for CBSE Board 2021 Exams only

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Example 8 Important Deleted for CBSE Board 2021 Exams only

Example 9 Deleted for CBSE Board 2021 Exams only

Example 10 Important Deleted for CBSE Board 2021 Exams only

Example 11

Example 12

Example 13 Important Deleted for CBSE Board 2021 Exams only

Example 14 Important Deleted for CBSE Board 2021 Exams only

Example 15 Important

Chapter 8 Class 12 Application of Integrals

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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.