Ex 7.4, 3 - Chapter 7 Class 12 Integrals

Transcript

Ex 7.4, 3 1/√((2 − 𝑥)^2 + 1) Let 2−𝑥=𝑡 Diff both sides w.r.t. x 0−1=𝑑𝑡/𝑑𝑥 𝑑𝑥=−𝑑𝑡 Integrating the function 𝑤.𝑟.𝑡.𝑥 ∫1▒1/√((2 − 𝑥)^2 + 1) 𝑑𝑥 Put the Values of 2−𝑥=𝑡 and 𝑑𝑥=−𝑑𝑡 =∫1▒(−𝑑𝑡)/√(𝑡^2 + 1) =−∫1▒𝑑𝑡/√(𝑡^2 +(1)^2 ) =−log⁡|𝑡+√(𝑡^2+1) |+𝐶 =log⁡〖|𝑡+√(𝑡^2+1) |^(−1) 〗+𝐶 =log⁡〖1/|𝑡 + √(𝑡^2 + 1) | 〗 +𝐶 =log⁡〖1/|2 − 𝑥 + √((2 − 𝑥)^2 + 1) | 〗 +𝐶 =log⁡〖1/|2 − 𝑥 + √(〖4 + 𝑥〗^2 − 4𝑥 + 1) | 〗 +𝐶 =𝒍𝒐𝒈⁡〖𝟏/|𝟐 − 𝒙 + √(𝒙^𝟐 − 𝟒𝒙 + 𝟓) | 〗 +𝑪