Ex 7.2, 26 - Integrate cos root(x) / root x - Teachoo - Ex 7.2

Ex 7.2, 26 - Chapter 7 Class 12 Integrals - Part 2

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Ex 7.2, 26 Integrate the function cos⁑√π‘₯/√π‘₯ Let √π‘₯=𝑑 Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ (1/2) π‘₯^(1/2 βˆ’ 1)= 𝑑𝑑/𝑑π‘₯ 1/2. π‘₯^(βˆ’ 1/2)= 𝑑𝑑/𝑑π‘₯ 1/(2√π‘₯) = 𝑑𝑑/𝑑π‘₯ 𝑑π‘₯ =2√π‘₯ . 𝑑𝑑 𝑑π‘₯ =2𝑑 . 𝑑𝑑 Integrating the function ∫1β–’γ€–" " cos⁑√π‘₯/√π‘₯ " " γ€—. 𝑑π‘₯ Putting √π‘₯=𝑑 & 𝑑π‘₯=2𝑑 . 𝑑𝑑 = ∫1β–’γ€–" " cos⁑𝑑/𝑑〗. 2𝑑 . 𝑑𝑑 = ∫1β–’γ€–" " 2 cos⁑𝑑 γ€—. 𝑑𝑑 = 2∫1β–’cos⁑𝑑 . 𝑑𝑑 = 2 sin⁑𝑑+𝐢 = 𝟐 π’”π’Šπ’β‘βˆšπ’™+π‘ͺ (π‘ˆπ‘ π‘–π‘›π‘” 𝑑=√π‘₯)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.