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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Ex 7.3, 1 Find the integral of sin2 (2𝑥 + 5) ∫1▒〖𝒔𝒊𝒏𝟐 (𝟐𝒙 + 𝟓) 〗 𝒅𝒙 =∫1▒(1 − 〖𝑐𝑜𝑠 2〗⁡(2𝑥 + 5))/2 𝑑𝑥 =1/2 ∫1▒〖1−cos⁡(4𝑥+10) 〗 𝑑𝑥 =1/2 [∫1▒1 𝑑𝑥−∫1▒cos⁡(4𝑥+10) 𝑑𝑥] We know that 𝐜𝐨𝐬 𝟐𝜽=𝟏−𝟐 〖𝒔𝒊𝒏〗^𝟐⁡𝜽 2 sin^2 𝜃=1−cos⁡2𝜃 sin^2 𝜃=1/2 [1−cos⁡2𝜃 ] Replace 𝜃 by (𝟐𝐱+𝟓) sin^2 (2𝑥+5)=(1 − cos⁡2(2𝑥 + 5))/2 As ∫1▒cos⁡(𝑎𝑥+𝑏) 𝑑𝑥=sin⁡(𝑎𝑥 + 𝑏)/𝑎+𝐶 =1/2 [𝑥− sin⁡(4𝑥 + 10)/4 +𝐶] =𝒙/𝟐 − 𝟏/𝟖 𝒔𝒊𝒏⁡(𝟒𝒙+𝟏𝟎)+𝑪

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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.