Ex 7.2, 39 (MCQ) - Chapter 7 Class 12 Integrals

Transcript

Ex 7.2, 39 ∫1▒𝑑𝑥/(𝑠𝑖𝑛2 𝑥 𝑐𝑜𝑠2 𝑥) equals tan x + cot x + C (B) tan x – cot x + C (C) tan x cot x + C (D) tan x – cot 2x + C ∫1▒〖" " 𝑑𝑥/(sin^2 𝑥 cos^2⁡𝑥 )〗 = ∫1▒〖" " 𝟏/(sin^2 𝑥 cos^2⁡𝑥 ) . 𝑑𝑥〗 = ∫1▒〖" " (〖𝐬𝐢𝐧〗^𝟐 𝒙 +〖 〖𝐜𝐨𝐬〗^𝟐〗⁡𝒙)/(sin^2 𝑥 cos^2⁡𝑥 ) . 𝑑𝑥〗 = ∫1▒〖" " (sin^2 𝑥)/(sin^2 𝑥 cos^2⁡𝑥 ) . 𝑑𝑥〗 + ∫1▒〖" " 〖 cos^2〗⁡𝑥/(sin^2 𝑥 cos^2⁡𝑥 ) . 𝑑𝑥〗 = ∫1▒〖" " 1/cos^2⁡𝑥 . 𝑑𝑥〗 + ∫1▒〖1/(sin^2 𝑥) . 𝑑𝑥〗 (Using sin^2⁡𝑥+cos^2⁡𝑥=1) = ∫1▒〖sec^2⁡𝑥. 𝑑𝑥〗 + ∫1▒〖𝑐𝑜𝑠𝑒𝑐^2 𝑥 . 𝑑𝑥〗 = 𝒕𝒂𝒏⁡𝒙−𝒄𝒐𝒕⁡𝒙+𝑪 ∴ Option B is correct. Using ∫1▒〖〖𝑠𝑒𝑐〗^2⁡𝑥. 𝑑𝑥〗=𝑡𝑎𝑛⁡𝑥 and ∫1▒〖𝑐𝑜𝑠𝑒𝑐^2 𝑥 . 𝑑𝑥〗=−𝑐𝑜𝑡⁡𝑥