Ex 7.3

Chapter 7 Class 12 Integrals
Serial order wise

### Transcript

Ex 7.3, 5 Integrate sin^3β‘π₯ cos^3 π₯ β«1βγsin^3β‘π₯ cos^3 π₯γ ππ₯ =β«1βγπ ππβ‘π₯. sin^2β‘π₯ cos^3 π₯γ ππ₯ =β«1βγπ ππβ‘π₯ (1βcos^2β‘π₯ ) cos^3 π₯γ ππ₯ =β«1βγ(1βcos^2β‘π₯ ) cos^3 π₯γ. π ππβ‘π₯ ππ₯ Let cosβ‘π₯=π‘ Differentiating w.r.t.x βsinβ‘π₯=ππ‘/ππ₯ ππ₯=ππ‘/(βsinβ‘π₯ ) (γπ ππγ^2β‘π=1βγπππ γ^2β‘π) β¦(1) Thus, our equation becomes β«1βγsin^2β‘π₯ cos^3 π₯γ ππ₯ =β«1βγ(1βcos^2β‘π₯ ) cos^3 π₯γ. π ππβ‘π₯ ππ₯" " =β«1βγ(1βπ‘^2 ) π‘^3 γ. π ππβ‘π₯Γ1/(βsinβ‘π₯ ) ππ‘" " =β«1βγβ(1βπ‘^2 ) π‘^3 γ ππ‘" " =ββ«1βγ(π‘^3βπ‘^5 ) γ ππ‘" " =β[β«1βπ‘^3 ππ‘ββ«1βπ‘^5 ππ‘] =β[π‘^(3 + 1)/(3 + 1) β π‘^(5 + 1)/(5 + 1)]+πΆ =β[π‘^4/4 β π‘^6/6]+πΆ =γβπ‘γ^4/4 + π‘^6/6+πΆ =π‘^6/6 β π‘^4/4 +πΆ Putting back value of π‘=πππ β‘π₯ =(γπππγ^π π)/π β (γπππγ^π π)/π +πͺ

#### 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.