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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.