Ex 7.6, 5 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Ex 7.6
Ex 7.6, 1
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Transcript
Ex 7.6, 5 𝑥 log2𝑥 Integrating the function 𝑤.𝑟.𝑡.𝑥 ∫1▒〖𝑥 log2𝑥 〗 𝑑𝑥 Hence, we take First function :- 𝑓(𝑥)=log(2𝑥) Second function :- g(𝑥)=𝑥 ∫1▒〖𝑥 log𝑥 〗 𝑑𝑥=∫1▒(log𝑥 )𝑥 𝑑𝑥 =log(2𝑥) ∫1▒𝑥 𝑑𝑥−∫1▒(𝑑(log2𝑥 )/𝑑𝑥 ∫1▒〖𝑥.𝑑𝑥〗)𝑑𝑥 =log(2𝑥) (𝑥^2/2)−∫1▒〖1/2𝑥 . 2 .𝑥^2/2. 𝑑𝑥〗 =〖𝑥^2/2 log〗(2𝑥)−∫1▒〖𝑥/2. 𝑑𝑥〗 =〖𝑥^2/2 log〗(2𝑥)−1/2 ∫1▒〖𝑥 𝑑𝑥〗 =〖𝑥^2/2 log〗(𝑥)− 1/2 (𝑥^2/2)+𝐶 =〖𝑥^2/2 log〗(2𝑥)− 𝑥^2/4 +𝐶
