Ex 7.8, 9 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by Teachoo

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Ex 7.8, 9 ∫_0^1▒𝑑𝑥/√(1−𝑥2) Step 1 :- Let F(𝑥)=∫1▒𝑑𝑥/√(1 − 𝑥^2 ) =∫1▒𝑑𝑥/√(1^2 − 𝑥^2 ) =sin^(−1)⁡〖𝑥/1〗 =𝑠𝑖𝑛^(−1) 𝑥 Hence F(𝑥)=𝑠𝑖𝑛^(−1) 𝑥 Step 2 :- ∫_0^1▒〖𝑑𝑥/√(1 − 𝑥^2 )=𝐹(1)−𝐹(0) 〗 =𝑠𝑖𝑛^(−1) (1)−𝑠𝑖𝑛^(−1) (0) =𝜋/2−0 =𝜋/2

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