1.

int_(0)^(2) x sqrt(x+2) dx " (put x+2 " =t^(2)")"

Answer»

Solution :`"LET B " x+2 =t^(2) rArr dx=2t dt`
`x=0 rArr t= sqrt(0+2)=sqrt(2)`
`x=2 rArr t=sqrt(2+2)=2`
`=int_(sqrt(2))^(2)(t^(2)-2)sqrt(t^(2)).2t dt= 2 int_(sqrt(2))^(2)(t^(4)-2t^(2))dt`
`=2[(t^(5))/(5)-(2t^(3))/(3)]_(sqrt(2))^(2)=(2)/(15)[3T^(5)-10t^(3)]_(sqrt(2))^(2)`
`=(2)/(15)[(96-80)-(12sqrt(2)-20sqrt(2))]`
`=(2)/(15)(16+8sqrt(2))=(16)/(15)(2+sqrt(2))`


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