Check sibling questions

Example 7 - Find intgeral (i) cos2 x dx (ii) sin 2x cos 3x

Example 7 - Chapter 7 Class 12 Integrals - Part 2
Example 7 - Chapter 7 Class 12 Integrals - Part 3

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Transcript

Example 7 Find (i) ∫1β–’cos^2⁑π‘₯ 𝑑π‘₯ ∫1β–’cos^2⁑π‘₯ 𝑑π‘₯ =∫1β–’((cos⁑2π‘₯ + 1)/2) 𝑑π‘₯ = 1/2 ∫1β–’(cos⁑2π‘₯+1) 𝑑π‘₯ = 1/2 [∫1β–’cos⁑2π‘₯ 𝑑π‘₯+∫1β–’1 𝑑π‘₯] We know cos⁑2π‘₯=2 cos^2⁑π‘₯βˆ’1 cos⁑2π‘₯+1=2 cos^2⁑π‘₯ (cos⁑2π‘₯ + 1)/2=cos^2⁑π‘₯ ∫1β–’π’„π’π’”β‘πŸπ’™ 𝒅𝒙 Let 2π‘₯=𝑑 2 =𝑑𝑑/𝑑π‘₯ 𝑑π‘₯=1/2 𝑑𝑑 ∫1β–’cos⁑𝑑 . 1/2 𝑑𝑑 =1/2 (sin⁑𝑑+𝐢1) Putting value of 𝑑 = 2π‘₯ =1/2 sin⁑2π‘₯+𝐢1 ∫1β–’πŸ 𝒅𝒙 =∫1β–’π‘₯^0 𝑑π‘₯ =[π‘₯^(0 + 1)/(0 + 1)]+𝐢 =π‘₯+𝐢2 Thus, ∫1β–’cos^2⁑π‘₯ 𝑑π‘₯=1/2 [∫1β–’cos⁑2π‘₯ 𝑑π‘₯+∫1β–’1 𝑑π‘₯] =1/2 [1/2 sin⁑2π‘₯+𝐢1+π‘₯+𝐢2] =1/4 sin⁑2π‘₯+π‘₯/2+1/2(𝐢1+𝐢2) =𝒙/𝟐+𝟏/πŸ’ π¬π’π§β‘πŸπ’™+π‘ͺ ("From (1) and (2) " ) ("Let" 𝐢1+𝐢2=𝐢)

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.