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Chapter 7 Class 12 Integrals
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Ex 7.6, 1 π‘₯ sin⁑π‘₯ ∫1β–’γ€–π‘₯ sin⁑π‘₯ γ€— 𝑑π‘₯ ∫1β–’γ€–π‘₯ sin⁑π‘₯ γ€— 𝑑π‘₯=𝒙 ∫1▒𝐬𝐒𝐧⁑𝒙 π’…π’™βˆ’βˆ«1β–’(𝒅(𝒙)/𝒅𝒙 ∫1β–’γ€–π’”π’Šπ’β‘π’™ 𝒅𝒙〗) 𝒅𝒙 = 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 " " Algebraic Trigonometric We know that ∫1▒〖𝑓(π‘₯) 𝑔⁑(π‘₯) γ€— 𝑑π‘₯=𝑓(π‘₯) ∫1▒𝑔(π‘₯) 𝑑π‘₯βˆ’βˆ«1β–’(𝑓^β€² (π‘₯) ∫1▒𝑔(π‘₯) 𝑑π‘₯) 𝑑π‘₯ Putting f(x) = x and g(x) = sin x

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