Ex 7.10

Chapter 7 Class 12 Integrals
Serial order wise

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### Transcript

Ex 7.10, 5 By using the properties of definite integrals, evaluate the integrals : β«_(β5)^5βγ |π₯+2| γ ππ₯ |π₯+2|={β((π₯+2) ππ π₯+2β₯0@β(π₯+2) ππ π₯+2<0)β€ ={β((π₯+2) ππ π₯β₯β,2@β(π₯+2) ππ π₯<β2)β€ β΄ β«_(β5)^5βγ|π₯+2|ππ₯=β«_(β5)^(β2)βγ|π₯+2|ππ₯+γγ β«_(β2)^5β|π₯+2|ππ₯ Using the Property P2 β«_π^πβγπ(π₯)ππ₯=β«_π^πβγπ(π₯)ππ₯+β«_π^πβπ(π₯)ππ₯γγ =β«_(β5)^(β2)βγβ(π₯+2)ππ₯+γ β«_(β2)^5β(π₯+2)ππ₯ =ββ«_(β5)^(β2)βγπ₯ππ₯βγ β«_(β5)^(β2)β2ππ₯+β«_(β2)^5βπ₯ππ₯+β«_(β2)^5β2ππ₯ =β[π₯^2/2]_(β5)^(β2)β2[π₯]_(β5)^(β2)+[π₯^2/2]_(β2)^5+2[π₯]_(β2)^5 =β(((β2)^2 β (β5)^2)/2)β2[β2β(β5)]+[((5)^2 β (β2)^2)/2] +2 [5β(β2)] =β((4 β 25)/2)β2[β2+5]+[(25 β 4)/2]+2[5+2] =β((β21)/2)β2[3]+21/2+2[7] =21/2+21/2β6+14 =42/2+8 = 21+8 = ππ