

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 7.10
Ex 7.10, 2
Ex 7.10, 3 Important
Ex 7.10, 4
Ex 7.10, 5 Important You are here
Ex 7.10, 6
Ex 7.10,7 Important
Ex 7.10,8 Important
Ex 7.10, 9
Ex 7.10, 10 Important
Ex 7.10, 11 Important
Ex 7.10, 12 Important
Ex 7.10, 13
Ex 7.10, 14
Ex 7.10, 15
Ex 7.10, 16 Important
Ex 7.10, 17
Ex 7.10, 18 Important
Ex 7.10, 19
Ex 7.10, 20 (MCQ) Important
Ex 7.10, 21 (MCQ) Important
Last updated at May 29, 2023 by Teachoo
Ex 7.10, 5 By using the properties of definite integrals, evaluate the integrals : β«_(β5)^5βγ |π₯+2| γ ππ₯ |π₯+2|={β((π₯+2) ππ π₯+2β₯0@β(π₯+2) ππ π₯+2<0)β€ ={β((π₯+2) ππ π₯β₯β,2@β(π₯+2) ππ π₯<β2)β€ β΄ β«_(β5)^5βγ|π₯+2|ππ₯=β«_(β5)^(β2)βγ|π₯+2|ππ₯+γγ β«_(β2)^5β|π₯+2|ππ₯ Using the Property P2 β«_π^πβγπ(π₯)ππ₯=β«_π^πβγπ(π₯)ππ₯+β«_π^πβπ(π₯)ππ₯γγ =β«_(β5)^(β2)βγβ(π₯+2)ππ₯+γ β«_(β2)^5β(π₯+2)ππ₯ =ββ«_(β5)^(β2)βγπ₯ππ₯βγ β«_(β5)^(β2)β2ππ₯+β«_(β2)^5βπ₯ππ₯+β«_(β2)^5β2ππ₯ =β[π₯^2/2]_(β5)^(β2)β2[π₯]_(β5)^(β2)+[π₯^2/2]_(β2)^5+2[π₯]_(β2)^5 =β(((β2)^2 β (β5)^2)/2)β2[β2β(β5)]+[((5)^2 β (β2)^2)/2] +2 [5β(β2)] =β((4 β 25)/2)β2[β2+5]+[(25 β 4)/2]+2[5+2] =β((β21)/2)β2[3]+21/2+2[7] =21/2+21/2β6+14 =42/2+8 = 21+8 = ππ