
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 7.3
Ex 7.3, 2
Ex 7.3, 3 Important
Ex 7.3, 4 Important
Ex 7.3, 5
Ex 7.3, 6 Important
Ex 7.3, 7
Ex 7.3, 8
Ex 7.3, 9 Important
Ex 7.3, 10 Important
Ex 7.3, 11
Ex 7.3, 12
Ex 7.3, 13 Important
Ex 7.3, 14
Ex 7.3, 15
Ex 7.3, 16 Important
Ex 7.3, 17
Ex 7.3, 18 Important
Ex 7.3, 19 Important
Ex 7.3, 20 Important
Ex 7.3, 21
Ex 7.3, 22 Important
Ex 7.3, 23 (MCQ)
Ex 7.3, 24 (MCQ) Important
Last updated at May 29, 2023 by Teachoo
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〗^𝟐𝜽 2 sin^2 𝜃=1−cos2𝜃 sin^2 𝜃=1/2 [1−cos2𝜃 ] Replace 𝜃 by (𝟐𝐱+𝟓) sin^2 (2𝑥+5)=(1 − cos2(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