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

### 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