1. Chapter 7 Class 12 Integrals (Term 2)
2. Concept wise
3. Integration by substitution - Trignometric - Normal

Transcript

Ex 7.2, 39 โซ1โ๐๐ฅ/(๐ ๐๐2 ๐ฅ ๐๐๐ 2 ๐ฅ) equals tan x + cot x + C (B) tan x โ cot x + C (C) tan x cot x + C (D) tan x โ cot 2x + C โซ1โใ" " ๐๐ฅ/(sin^2 ๐ฅ cos^2โก๐ฅ )ใ = โซ1โใ" " ๐/(sin^2 ๐ฅ cos^2โก๐ฅ ) . ๐๐ฅใ = โซ1โใ" " (ใ๐ฌ๐ข๐งใ^๐ ๐ +ใ ใ๐๐จ๐ฌใ^๐ใโก๐)/(sin^2 ๐ฅ cos^2โก๐ฅ ) . ๐๐ฅใ = โซ1โใ" " (sin^2 ๐ฅ)/(sin^2 ๐ฅ cos^2โก๐ฅ ) . ๐๐ฅใ + โซ1โใ" " ใ cos^2ใโก๐ฅ/(sin^2 ๐ฅ cos^2โก๐ฅ ) . ๐๐ฅใ = โซ1โใ" " 1/cos^2โก๐ฅ . ๐๐ฅใ + โซ1โใ1/(sin^2 ๐ฅ) . ๐๐ฅใ (Using sin^2โก๐ฅ+cos^2โก๐ฅ=1) = โซ1โใsec^2โก๐ฅ. ๐๐ฅใ + โซ1โใ๐๐๐ ๐๐^2 ๐ฅ . ๐๐ฅใ = ๐๐๐โก๐โ๐๐๐โก๐+๐ช โด Option B is correct. Using โซ1โใใ๐ ๐๐ใ^2โก๐ฅ. ๐๐ฅใ=๐ก๐๐โก๐ฅ and โซ1โใ๐๐๐ ๐๐^2 ๐ฅ . ๐๐ฅใ=โ๐๐๐กโก๐ฅ