Ex 7.3, 20 - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
Ex 7.3
Ex 7.3, 1
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Transcript
Ex 7.3, 20 Integrate the function cosβ‘2π₯/(cosβ‘γπ₯ γ+ sinβ‘π₯ )^2 β«1βcosβ‘2π₯/(cosβ‘π₯ + sinβ‘π₯ )^2 =β«1β(cos^2β‘π₯ β sin^2β‘π₯)/(cosβ‘π₯ + sinβ‘π₯ )^2 ππ₯ =β«1β(cosβ‘π₯ β sinβ‘π₯ )(cosβ‘π₯ + sinβ‘π₯ )/(cosβ‘π₯ + sinβ‘π₯ )^2 ππ₯ =β«1β(cosβ‘π₯ β sinβ‘π₯)/(cosβ‘π₯ + sinβ‘π₯ ) ππ₯ Let cosβ‘π₯+sinβ‘π₯=π‘ Differentiating w.r.t. x (πππ β‘2π=γπππ γ^2β‘πβγπ ππγ^2β‘π) βsinβ‘π₯+cosβ‘π₯=ππ‘/ππ₯ (cosβ‘π₯βsinβ‘π₯ )ππ₯=ππ‘ ππ₯=1/((cosβ‘π₯ β sinβ‘π₯ ) ) ππ‘ Thus, our equation becomes =β«1β((cosβ‘π₯ β sinβ‘π₯ ))/π‘ Γππ‘/(cosβ‘π₯ β sinβ‘π₯ ) =β«1β1/π‘ ππ‘ =logβ‘|π‘|+πΆ Putting value of π‘=πππ β‘π₯+π ππβ‘π₯ =πππβ‘|πππβ‘π+πππβ‘π |+πͺ
