1.

`int(x^(7m)+x^(2m)+x^m)(2x^(6m)+7x^m+14)^(1/m)dx`A. `(7x^(7m)+2x^(2m)+14x^(m))^((m+1)/(m))/(14(m+1))+C`B. `(2x^(7m)+14x^(2m)+7x^(m))^((m+1)/(m))/(14(m+1))+C`C. `(2x^(7m)+7x^(2m)+14x^(m))^((m+1)/(m))/(14(m+1))+C`D. `(7x^(7m)+2x^(2m)+x^(m))^((m+1)/(m))/(14(m+1))+C`

Answer» Correct Answer - c
Let `I=int(x^(7m)+x^(2m)+x^(m))(2x^(6m)+7x^(m)+14)^(1//m)dx`. then ,
`I=int(x^(7m-1)+x^(2m-1)+x^(m-1))(2x^(7m)+7x^(2m)+14x^(m))^(1//m)dx` Let `2x^(7m)+7x^(2m)+14x^(m)=t` . then,
`14m(x^(7m-1)+x^(2m-1)+x^(m-1))dx =dt`
`I=(1)/(14m)int^(t^(1//m))dt=(1)/(14m)(t^(1/(m)+1))/(((1)/(m)+1))+C`
`rArrI=(1)/(14(m+1))(2x^(7m)+7x^(2m)+14x^(m))^((m+1)/(m))+C`


Discussion

No Comment Found

Related InterviewSolutions