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Ex 7.2, 4 - Integrate sin x. sin (cos x) - CBSE - Integration by substitution - Trignometric - Normal

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.2, 4 Integrate the function: sin⁑π‘₯. sin ⁑(cos⁑π‘₯) Step 1: Let cos⁑π‘₯ = 𝑑 Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ βˆ’sin⁑π‘₯=𝑑𝑑/𝑑π‘₯ 𝑑π‘₯=𝑑𝑑/(βˆ’sin⁑π‘₯ ) Step 2: Integrating function ∫1β–’γ€–sin⁑π‘₯ . sin⁑〖 (cos⁑π‘₯ )γ€— γ€—. 𝑑π‘₯ Putting values of t & dt =∫1β–’γ€–sin⁑π‘₯ . sin⁑𝑑〗 . 𝑑𝑑/(βˆ’sin⁑π‘₯ ) =βˆ’βˆ«1β–’γ€–sin⁑𝑑〗 . 𝑑𝑑 =βˆ’(βˆ’cos⁑𝑑+𝐢) =cos⁑𝑑+𝐾 Putting 𝑑=π‘π‘œπ‘ β‘π‘₯ =𝒄𝒐𝒔⁑(πœπ¨π¬β‘π’™ )+𝑲

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