Example 24 - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
Examples
Example 1 (i)
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Chapter 7 Class 12 Integrals
Serial order wise
Transcript
Example 24 Find β«1ββ(3β2π₯βπ₯^2 ) ππ₯ β«1βγβ(3β2π₯βπ₯^2 ) ππ₯γ =β«1ββ(3β(2π₯+π₯^2 ) ) ππ₯ Adding and Subtracting 1^2 =β«1ββ(3β(π₯^2+2π₯+1^2β1^2 ) ) ππ₯ =β«1ββ(3β(π₯^2+2π₯+1^2 )+1) ππ₯ =β«1ββ(3+1β(π₯^2+2π₯+1^2 ) ) ππ₯ =β«1ββ(4β(π₯^2+2π₯+1^2 ) ) ππ₯ =β«1ββ(2^2β(π₯+1)^2 ) ππ₯ It is of the form β«1βγβ(π^2βπ₯^2 ) ππ₯=1/2 π₯β(π^2βπ₯^2 )+π^2/2 π ππ^(β1) π₯/π+πΆγ Replacing a with 2 and π₯ with (π₯+1) =1/2 (π₯+1) β(2^2β(π₯+1)^2 )+2^2/2 π ππ^(β1) ((π₯ + 1))/2+πΆ =1/2 (π₯+1) β(4β(π₯^2+1^2+2π₯))+2π ππ^(β1) ((π₯ + 1))/2+πΆ =π/π (π+π) β(πβππβπ^π )+π πππ^(βπ) ((π + π))/π+πͺ
