Ex 7.11

Chapter 7 Class 12 Integrals
Serial order wise

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### Transcript

Ex 7.11,7 By using the properties of definite integrals, evaluate the integrals : β«_0^1βγ π₯(1βπ₯)^π γ ππ₯ Let I=β«_0^1βγπ₯(1βπ₯)^π ππ₯γ β΄ I=β«_0^1βγ(1βπ₯) [1β(1βπ₯)]^π ππ₯γ I=β«_0^1βγ(1βπ₯) [1β1+π₯]^π ππ₯γ I=β«_0^1βγ(1βπ₯) [π₯]^π ππ₯γ I= β«_0^1βγ(1βπ₯) γ π₯γ^π ππ₯γ Using P4 : β«_0^πβγπ(π₯)ππ₯=γ β«_0^πβπ(πβπ₯)ππ₯ I= β«_0^1βγ(γ π₯γ^πβ π₯^(π + 1) ) ππ₯γ I= β«_0^1βγγ π₯γ^π ππ₯γββ«_0^1βγγ π₯γ^(π + 1) ππ₯γ I=[π₯^(π + 1)/(π + 1)]_0^1β[π₯^(π + 2)/(π + 2)]_0^1 I=[(1)^(π + 1)/(π + 1)β(0)^(π + 1)/(π + 1)]β[(1)^(π + 2)/(π + 2)β(0)^(π + 2)/(π + 2)] I= 1/(π + 1)β1/(π + 2) I=(π + 2 β (π + 1))/(π + 1)(π + 2) π=π/(π + π)(π + π)