Examples

Chapter 7 Class 12 Integrals
Serial order wise

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### Transcript

Example 9 Find the following integrals: (iii) β«1βππ₯/(β(5π₯^2 β 2π₯) ) β«1βππ₯/(β(5π₯^2 β 2π₯) ) = β«1βππ₯/(β(5(π₯^2 β 2/5 π₯) ) ) = β«1βππ₯/(β(5(π₯^2 β 2(π₯)(1/5)) ) ) = β«1βππ₯/(β(5(π₯^2 β 2(π₯)(1/5) + (1/5)^2β (1/5)^2 ) ) ) = β«1βππ₯/(β(5[(π₯ β 1/5)^2β(1/5)^2 ] ) ) = β«1βππ₯/(β5 β((π₯ β 1/5)^2β(1/5)^2 )) (Taking 5 common) [Adding and subtracting (1/5)^2] = β«1βππ₯/(β(5[(π₯ β 1/5)^2β(1/5)^2 ] ) ) = β«1βππ₯/(β5 β((π₯ β 1/5)^2β(1/5)^2 )) =1/β5 πππ|π₯β1/5+β((π₯β1/5)^2β(1/5)^2 )|+πΆ =1/β5 πππ|π₯β1/5+β(π₯^2+(1/5)^2β2(π₯)(1/5)β(1/5)^2 )|+πΆ =π/βπ πππ|πβπ/π+β(π^πβππ/π)|+πͺ It is of form β«1βγππ₯/(β(π₯^2 β π^2 ) )=πππ|π₯+β(π₯^2βπ^2 )|+πΆ1γ Replacing π₯ by (π₯β1/5)πππ π ππ¦ 1/5, (Usingβ(π.π)=βπ βπ)