Ex 7.6, 1 - Find integration of x sin x - Chapter 7 Class 12 - Integration by parts

  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

Ex 7.6, 1 - Chapter 7 Class 12 Integration - NCERT Book Integrate x sin x ∫ x sin x dx | | Algebraic Trigonometric We solve this by Integration by parts We know that ∫ f(x) g(x) dx = f(x) βˆ«π‘”(π‘₯) 𝑑π‘₯ βˆ’ ∫(𝑓′ (π‘₯) ∫ 𝑔(π‘₯) 𝑑π‘₯) 𝑑π‘₯ Putting f(x) = x and g(x) = sin x ∫1β–’γ€–π‘₯ sin⁑π‘₯ γ€— 𝑑π‘₯=π‘₯ ∫1β–’sin⁑π‘₯ 𝑑π‘₯βˆ’βˆ«1β–’(𝑑(π‘₯)/𝑑π‘₯ ∫1β–’γ€–sin⁑π‘₯ 𝑑π‘₯γ€—) 𝑑π‘₯ = βˆ’ π‘₯ cos⁑π‘₯ βˆ’ ∫1β–’γ€–βˆ’cos⁑〖π‘₯ 𝑑π‘₯γ€— γ€— = βˆ’ π‘₯ cos⁑π‘₯+ ∫1β–’γ€–cos⁑π‘₯+𝐢〗 = βˆ’ 𝒙 𝒄𝒐𝒔⁑𝒙+π’”π’Šπ’β‘π’™+π‘ͺ

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