Ex 7.10

Chapter 7 Class 12 Integrals
Serial order wise

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### Transcript

Ex 7.10, 18 By using the properties of definite integrals, evaluate the integrals : β«_0^4β|π₯β1| ππ₯ |π₯β1|= {β( (π₯β1) ππ π₯β1β₯0@β(π₯β1) ππ π₯β1<0)β€ = {β((π₯β1,) ππ π₯β₯1@β(π₯β1) ππ π₯<1)β€ β΄ β«_0^4β|π₯β1|ππ₯=β«_0^1β|π₯β1|ππ₯+β«_1^4β|π₯β1|ππ₯ Using the property, P2 P2 :- β«_π^πβγπ(π₯)ππ₯=γ β«_π^πβγπ(π₯)ππ₯+β«_π^πβπ(π₯)ππ₯γ =β«_0^1βγβ(π₯β1)ππ₯+γ β«_1^4β(π₯β1)ππ₯ =β«_0^1βγ(βπ₯+1)ππ₯+γ β«_1^4β(π₯β1)ππ₯ =β«_0^1βγβπ₯ ππ₯+γ β«_0^1βγ1. ππ₯+β«_1^4βγπ₯ . ππ₯ββ«_1^4βγ1.ππ₯γγγ =β[π₯^2/2]_0^1+[π₯]_0^1β[π₯^2/2]_1^4β[π₯]_1^4 =β[((1)^2 β 0)/2]+[1β0]+[((4)^2β(1)^2)/2]β[4β1] =β1/2+1+[(16 β 1)/2]β3 =β1/2+15/2β3+1 =(14 )/2β2= 7 β 2 = 5