Integration Full Chapter Explained - Integration Class 12 - Everything you need



  1. Chapter 7 Class 12 Integrals
  2. Serial order wise


Ex 7.1, 5 Find anti derivative of sin⁑2π‘₯ – 4𝑒3π‘₯ Subtracting (1) & (2) sin⁑2π‘₯βˆ’γ€–4𝑒〗^3π‘₯=(βˆ’1)/2 (cos⁑2π‘₯ )^β€²βˆ’ 4/3 (𝑒^3π‘₯ )^β€² We know that (cos⁑2π‘₯ )^β€²=βˆ’2 sin⁑2π‘₯ (βˆ’1)/2 (cos⁑2π‘₯ )^β€²=sin⁑2π‘₯ 𝐬𝐒𝐧 πŸπ’™=(βˆ’πŸ)/𝟐 (π’„π’π’”β‘πŸπ’™ )^β€² We know that (𝑒^3π‘₯ )^β€²=𝑒^3π‘₯ . 3 β‡’ γ€–1(𝑒^3π‘₯ )γ€—^β€²/3=𝑒^3π‘₯ ⇒𝑒^3π‘₯=γ€–1(𝑒^3π‘₯ )γ€—^β€²/3 β‡’γ€–πŸ’π’†γ€—^πŸ‘π’™=πŸ’/πŸ‘ (𝒆^πŸ‘π’™ )^β€² …(2) =(βˆ’1/2 cos⁑2π‘₯βˆ’4/3 𝑒^3π‘₯ )^β€² ∴ Anti derivative is (βˆ’πŸ)/𝟐 π’„π’π’”β‘πŸπ’™βˆ’ πŸ’/πŸ‘ 𝒆^πŸ‘π’™

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.