Homework Help

Evaluate by substitution. `int_0^ax(sqrt(x^2+a^2))dx`, a>0Evaluate by substitution....

user profile pic

user6978788 | Student, Undergraduate | (Level 1) Honors

Posted February 7, 2013 at 9:18 PM via web

dislike 2 like

Evaluate by substitution. `int_0^ax(sqrt(x^2+a^2))dx`, a>0

Evaluate by substitution. `int_0^ax(sqrt(x^2+a^2))dx` , a>0. The answer says it should be `1/3(2sqrt(2)-1)a^3` , how come?

1 Answer | Add Yours

Top Answer

user profile pic

tiburtius | High School Teacher | (Level 1) Educator

Posted February 7, 2013 at 10:18 PM (Answer #1)

dislike 1 like


Our substitution is `t=x^2+a^2` and our new limits of integration are `t_1` and `t_2`.

`1/2int_(a^2)^(2a^2)sqrt t dt=1/2cdot2/3t^(3/2)|_(a^2)^(2a^2)=1/3(2^(3/2)a^3-a^3)=1/3(2sqrt2-1)a^3`` `

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes