Ex 7.6, 1 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by Teachoo

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Ex 7.6, 1 𝑥 sin⁡𝑥 ∫1▒〖𝑥 sin⁡𝑥 〗 𝑑𝑥 ∫1▒〖𝑥 sin⁡𝑥 〗 𝑑𝑥=𝒙 ∫1▒𝐬𝐢𝐧⁡𝒙 𝒅𝒙−∫1▒(𝒅(𝒙)/𝒅𝒙 ∫1▒〖𝒔𝒊𝒏⁡𝒙 𝒅𝒙〗) 𝒅𝒙 = − 𝑥 cos⁡𝑥 − ∫1▒〖−cos⁡〖𝑥 𝑑𝑥〗〗 = − 𝑥 cos⁡𝑥+ ∫1▒〖cos⁡𝑥+𝐶〗 = − 𝒙 𝒄𝒐𝒔⁡𝒙+𝒔𝒊𝒏⁡𝒙+𝑪 " " Algebraic Trigonometric We know that ∫1▒〖𝑓(𝑥) 𝑔⁡(𝑥) 〗 𝑑𝑥=𝑓(𝑥) ∫1▒𝑔(𝑥) 𝑑𝑥−∫1▒(𝑓^′ (𝑥) ∫1▒𝑔(𝑥) 𝑑𝑥) 𝑑𝑥 Putting f(x) = x and g(x) = sin x

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