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Ex 7.1, 5 - Find anti-derivative of sin 2x - 4 e^3x - Chapter 7

Ex 7.1, 5 - Chapter 7 Class 12 Integrals - Part 2

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.