Check sibling questions

Ex 7.4, 13 - Integrate 1 / root (x - 1) (x - 2) - Integration by specific formulaes - Formula 4

Ex 7.4, 13 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.4, 13 - Chapter 7 Class 12 Integrals - Part 3


Transcript

Ex 7.4, 13 1/√((𝑥 − 1)(𝑥 − 2)) Integrating the function 𝑤.𝑟.𝑡.𝑥 ∫1▒1/√((𝑥 − 1)(𝑥 − 2)) 𝑑𝑥 =∫1▒1/√(𝑥(𝑥 − 2) − 1 (𝑥 − 2) ) 𝑑𝑥 =∫1▒1/√(𝑥^2 − 2𝑥 − 𝑥 + 2) 𝑑𝑥 =∫1▒1/√(𝑥^2 − 3𝑥 + 2) 𝑑𝑥 =∫1▒1/√(𝑥^2 − 2(3/2)(𝑥) + 2) 𝑑𝑥 =∫1▒1/√(𝑥^2 − 2(3/2)(𝑥) + (3/2)^2− (3/2)^2+ 2) 𝑑𝑥 =∫1▒1/√((𝑥 − 3/2)^2 − (3/2)^2 + 2) 𝑑𝑥 =∫1▒1/√((𝑥 − 3/2)^2 − 9/4 + 2) 𝑑𝑥 =∫1▒1/√((𝑥 − 3/2)^2 − 1/4 ) 𝑑𝑥 =∫1▒1/√((𝑥 − 3/2)^2 − (1/2)^2 ) 𝑑𝑥 =𝑙𝑜𝑔⁡|𝑥− 3/2+√((𝑥− 3/2)^2 − (1/2)^2 )|+𝐶 =𝑙𝑜𝑔⁡|𝑥− 3/2+√(𝑥^2+(3/2)^2−2(𝑥)(3/2)− 1/4)|+𝐶 =𝑙𝑜𝑔⁡|𝑥− 3/2+√(𝑥^2+9/4−3𝑥− 1/4)|+𝐶 =𝑙𝑜𝑔⁡|𝑥− 3/2+√(𝑥^2−3𝑥+9/4− 1/4)|+𝐶 =𝑙𝑜𝑔⁡|𝑥− 3/2+√(𝑥^2−3𝑥+8/4)|+𝐶 =𝒍𝒐𝒈⁡|𝒙− 𝟑/𝟐+√(𝒙^𝟐−𝟑𝒙+𝟐)|+𝑪

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.