Ex 7.7, 8 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by Teachoo

Ex 7.7, 8 - Integrate root x2 + 3x - Chapter 7 CBSE NCERT

Ex 7.7, 8 - Chapter 7 Class 12 Integrals - Part 2

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Transcript

Ex 7.7, 8 √(𝑥2+3𝑥) ∫1▒〖√(𝑥^2+3𝑥) 𝑑𝑥〗 =∫1▒〖√(𝑥^2+2(3/2)(𝑥) ) 𝑑𝑥〗 =∫1▒〖√(𝑥^2+2(3/2)(𝑥)+(3/2)^2−(3/2)^2 ) 𝑑𝑥〗 =∫1▒〖√((𝑥+3/2)^2−(3/2)^2 ) 𝑑𝑥〗 It is of the form ∫1▒〖√(𝑥^2−𝑎^2 ) 𝑑𝑥=𝑥/2 √(𝑥^2−𝑎^2 )−𝑎^2/2 𝑙𝑜𝑔|𝑥+√(𝑥^2−𝑎^2 )|+𝐶〗 ∴ Replacing 𝑥 by 𝑥+3/2 and a by 3/2 , we get =(𝑥 + 3/2)/2 √((𝑥+3/2)^2−(3/2)^2 )−|𝑥+3/2+√((𝑥+𝑥/2)^2−(3/2)^2 )|+𝐶 =(2𝑥 + 3)/4 √((𝑥+3/2)^2−9/4) − 9/8 𝑙𝑜𝑔|𝑥+3/2 √((𝑥+3/2)^2−9/4)|+𝐶 =(2𝑥 + 3)/4 √(𝑥^2+9/4+2(𝑥)(3/2)−9/4) − 9/8 𝑙𝑜𝑔|𝑥+3/2+√(𝑥^2+9/4+2 (𝑥)(3/2)−9/4)|+𝐶 =(2𝑥 + 3)/4 √(𝑥^2+2𝑥(3/2) )− 9/8 𝑙𝑜𝑔|𝑥+3/2+√(𝑥^2+2𝑥(3/2) )|+𝐶 =(𝟐𝒙 + 𝟑)/𝟒 √(𝒙^𝟐+𝟑𝒙)− 𝟗/𝟖 𝒍𝒐𝒈|𝒙+𝟑/𝟐+√(𝒙^𝟐+𝟑𝒙)|+𝑪

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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