CBSE Class 12 Sample Paper for 2022 Boards (For Term 2)

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## Find f sin 2 x/ 9 - cos4 x dx

This question is similar to Example 42 - Chapter 7 Class 12 - Integrals

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### Transcript

Question 1 β Choice 2 Find β«1βγsinβ‘2π₯/β(9 β cos^4β‘π₯ ) ππ₯γNow, β«1βγsinβ‘2π₯/β(9 β cos^4β‘π₯ ) ππ₯γ=β«1βγ(π π¬π’π§β‘π ππ¨π¬β‘π)/β(π β(γπππγ^πβ‘π )^π ) ππγ Let γπππγ^πβ‘π=π Differentiating both sides w.r.t.π₯ 2 cosβ‘π₯ Γ βsinβ‘π₯=ππ‘/ππ₯ ππ=ππ/(βπ πππβ‘π πππβ‘π ) Hence, our equation becomes β«1βγ(π π¬π’π§β‘π ππ¨π¬β‘π)/β(π β(γπππγ^πβ‘π )^π ) ππγ =β«1βγ(2 sinβ‘π₯ cosβ‘π₯)/β(9 β π‘^2 ) ππ₯γ =β«1βγ(2 sinβ‘π₯ cosβ‘π₯)/β(9 β π‘^2 )Γππ/(βπ πππβ‘π πππβ‘π )γ =ββ«1βππ‘/β((3)^2 β (π‘)^2 ) =β[sin^(β1)β‘γπ‘/3+πΆ1γ ] =βπππ^(βπ) π/π+πͺ It is of form β«1βγππ/β(π^π β π^π )=πππ^(βπ) π/π+πͺγ Replacing π₯ by π‘ and π by 3, we get Putting back π=γπππγ^πβ‘π =βπππ^(βπ) [π/π π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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.