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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 1 Find the area enclosed by the circle 𝑥2 + 𝑦2 = 𝑎2Given 𝑥^2 + 𝑦^2= 𝑎^2 This is a circle with Center = (0, 0) Radius = 𝑎 Since radius is a, OA = OB = 𝑎 A = (𝑎, 0) B = (0, 𝑎) Now, Area of circle = 4 × Area of Region OBAO = 4 × ∫1_𝟎^𝒂▒〖𝒚 𝒅𝒙〗 Here, y → Equation of Circle We know that 𝑥^2 + 𝑦^2 = 𝑎^2 𝑦^2 = 𝑎^2− 𝑥^2 y = ± √(𝑎^2−𝑥^2 ) Since AOBA lies in 1st Quadrant y = √(𝒂^𝟐−𝒙^𝟐 ) Now, Area of circle = 4 × ∫1_0^𝑎▒〖𝑦 𝑑𝑥〗 = 4 × ∫1_0^𝑎▒〖√(𝑎^2−𝑥^2 ) 𝑑𝑥〗 Using: √(𝑎^2−𝑥^2 )dx = 1/2 √(𝑎^2−𝑥^2 ) + 𝑎^2/2 〖"sin" 〗^(−1) 𝑥/4 + c = 4[𝒙/𝟐 √(𝒂^𝟐−𝒙^𝟐 )+𝒂^𝟐/𝟐 〖"sin" 〗^(−𝟏) 𝒙/𝒂]_𝟎^𝒂 = 4[𝑎/2 √(𝑎^2−𝑎^2 )+𝑎^2/2 〖"sin" 〗^(−1) 𝑎/𝑎−0/2 √(𝑎^2−0)−0^2/2 〖"sin" 〗^(−1) (0)] = 4[0+𝑎^2/2 〖"sin" 〗^(−1) (1)−0−0] = 4.𝑎^2/2. 𝜋/2 = 𝝅𝒂^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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.