Integration using trigo identities - 2x formulae

Chapter 7 Class 12 Integrals
Concept wise

### Transcript

Ex 7.3, 1 Find the integral of sin2 (2π₯ + 5) β«1βγππππ (ππ + π) γ ππ =β«1β(1 β γπππ  2γβ‘(2π₯ + 5))/2 ππ₯ =1/2 β«1βγ1βcosβ‘(4π₯+10) γ ππ₯ =1/2 [β«1β1 ππ₯ββ«1βcosβ‘(4π₯+10) ππ₯] We know that ππ¨π¬ ππ½=πβπ γπππγ^πβ‘π½ 2 sin^2 π=1βcosβ‘2π sin^2 π=1/2 [1βcosβ‘2π ] Replace π by (ππ±+π) sin^2 (2π₯+5)=(1 β cosβ‘2(2π₯ + 5))/2 As β«1βcosβ‘(ππ₯+π) ππ₯=sinβ‘(ππ₯ + π)/π+πΆ =1/2 [π₯β sinβ‘(4π₯ + 10)/4 +πΆ] =π/π β π/π πππβ‘(ππ+ππ)+πͺ

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.