# Misc 7 - Chapter 7 Class 12 Integrals

Last updated at Dec. 24, 2018 by Teachoo

Last updated at Dec. 24, 2018 by Teachoo

Transcript

Misc 7 Integrate the function sinβ‘π₯/sinβ‘(π₯ β π) Let I = β«1βsinβ‘π₯/sinβ‘(π₯ β π) ππ₯ Put t = π₯ β π Differentiating π€.π.π‘.π₯ ππ‘/ππ₯ = π(π₯ β π)/ππ₯ ππ‘/ππ₯ = 1 ππ₯ = ππ‘ Therefore β«1βγsin γβ‘(π‘ + π)/sinβ‘π‘ ππ‘ = β«1β(sinβ‘π‘ cosβ‘π + cosβ‘π‘ sinβ‘π)/sinβ‘π‘ ππ‘ = β«1β((sinβ‘π‘ cosβ‘π)/sinβ‘π‘ + (cosβ‘π‘ sinβ‘π)/sinβ‘π‘ ) ππ‘ = β«1βcosβ‘π ππ‘ + β«1βcotβ‘π‘ sinβ‘π ππ‘ = cosβ‘π β«1βππ‘ + sinβ‘π β«1βcotβ‘π‘ ππ‘ = t cos a + sin a log |sinβ‘π‘ | + C Putting back t = x β a = (x β a) cos a + sin a |sinβ‘γ(π₯βπ)γ | + C = sin a log |sinβ‘γ(π₯βπ)γ | + x cos a β a cos a + C = sin a log |π¬π’π§β‘γ(πβπ)γ | + x cos a + π_π

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Integration Formula Sheet - Chapter 7 Class 12 Formulas Important

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.