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Ex 7.4, 5 - Integrate 3x / 1 + 2x4 - Chapter 7 Class 12 - Integration by specific formulaes - Formula 3

Ex 7.4, 5 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.4, 5 - Chapter 7 Class 12 Integrals - Part 3


Transcript

Ex 7.4, 5 3𝑥/(1 + 2𝑥4) Let 𝑥^2=𝑡 Differentiating both sides 2𝑥=𝑑𝑡/𝑑𝑥 𝑑𝑥=𝑑𝑡/2𝑥 Integrating the function 𝑤.𝑟.𝑡.𝑥 ∫1▒(3𝑥 )/(1 + 2𝑥^4 ) 𝑑𝑥 =∫1▒3𝑥/(1 + 2(𝑥^2 )^2 ) 𝑑𝑥 Putting value of 𝑥^2=𝑡 and 𝑑𝑥=𝑑𝑡/2𝑥 =∫1▒3𝑥/(1 + 2𝑡^2 ) 𝑑𝑥 =∫1▒3𝑥/(1 + 2𝑡^2 )×𝑑𝑡/2𝑥 =3/2 ∫1▒𝑑𝑡/(1 + 2𝑡^2 ) =3/2 ∫1▒𝑑𝑡/2(1/2 + 𝑡^2 ) =3/(2 . 2) ∫1▒𝑑𝑡/(1/2 + 𝑡^2 ) =3/4 ∫1▒𝑑𝑡/(𝑡^2 + 1/2). 𝑑𝑡 =3/4 ∫1▒𝑑𝑡/(𝑡^2 +(1/√2)^2 ). 𝑑𝑡

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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.