Find ∫ 𝑒 𝑥 (1 − cot 𝑥 + 𝑐𝑜𝑠𝑒𝑐 2 𝑥) 𝑑
CBSE Class 12 Sample Paper for 2021 Boards
CBSE Class 12 Sample Paper for 2021 Boards
Last updated at Dec. 16, 2024 by Teachoo
Question 7 (Choice 1) Find ∫ 𝑒𝑥 (1 − cot 𝑥 + 𝑐𝑜𝑠𝑒𝑐2𝑥) 𝑑x ∫ 𝑒𝑥 ( [1 − cot 𝑥] + 𝑐𝑜𝑠𝑒𝑐2𝑥) 𝑑x It is of the form ∫1▒〖𝒆^𝒙 [𝒇(𝒙)+𝒇^′ (𝒙)] 〗 𝒅𝒙=𝒆^𝒙 𝒇(𝒙)+𝑪 Where 𝑓(𝑥)=1−cot𝑥 𝑓^′ (𝑥)=0−(−𝑐𝑜𝑠𝑒𝑐^2 𝑥)=𝑐𝑜𝑠𝑒𝑐^2 𝑥 So, our equation becomes ∫ 𝑒𝑥 ( [1 − cot 𝑥] + 𝑐𝑜𝑠𝑒𝑐2𝑥) 𝑑x" " = 𝒆^𝒙 (𝟏−𝒄𝒐𝒕 𝒙) +𝑪