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Ex 7.6
Ex 7.6, 2 Important
Ex 7.6, 3
Ex 7.6, 4
Ex 7.6, 5 Important You are here
Ex 7.6, 6
Ex 7.6, 7 Important
Ex 7.6, 8
Ex 7.6, 9
Ex 7.6, 10 Important
Ex 7.6, 11
Ex 7.6, 12
Ex 7.6, 13 Important
Ex 7.6, 14 Important
Ex 7.6, 15
Ex 7.6, 16
Ex 7.6, 17
Ex 7.6, 18 Important
Ex 7.6, 19
Ex 7.6, 20 Important
Ex 7.6, 21
Ex 7.6, 22 Important
Ex 7.6, 23 (MCQ)
Ex 7.6, 24 (MCQ) Important
Last updated at March 16, 2023 by Teachoo
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