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Chapter 7 Class 12 Integrals (Term 2)
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Ex 7.2, 23 - Integrate sin-1 x / root(1 - x2) - Class 12 - Integration by substitution - Trignometric - Inverse

Ex 7.2, 23 - Chapter 7 Class 12 Integrals - Part 2


Transcript

Ex 7.2, 23 sin^(βˆ’1)⁑π‘₯/√(1 βˆ’ π‘₯^2 ) Step 1: Let sin^(βˆ’1)⁑π‘₯=𝑑 Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ 1/√(1 βˆ’ π‘₯^2 )= 𝑑𝑑/𝑑π‘₯ 𝑑π‘₯=√(1 βˆ’ π‘₯^2 ) .𝑑𝑑 Step 2: Integrating the function ∫1β–’γ€–" " sin^(βˆ’1)⁑π‘₯/√(1 βˆ’ π‘₯^2 ) " " γ€—. 𝑑π‘₯ putting sin^(βˆ’1)⁑π‘₯=𝑑 & 𝑑π‘₯=√(1 βˆ’ π‘₯^2 ) .𝑑𝑑 = ∫1▒〖𝑑/√(1 βˆ’ π‘₯^2 ) " " γ€—. √(1 βˆ’ π‘₯^2 ) .𝑑𝑑 = ∫1▒〖𝑑 . 𝑑𝑑〗 = 𝑑^2/2+𝐢 = (γ€–π’”π’Šπ’γ€—^(βˆ’πŸ)⁑𝒙 )^𝟐/𝟐+π‘ͺ

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