Integration by parts and substitution help (1 Viewer)

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Integration by parts and substitution help!!

1. The problem statement, all variables and given/known data


∫0
-1 e ^√x+1




2. Relevant equations



3. The attempt at a solution
 

HallsofIvy

Science Advisor
41,626
821
Re: Integration by parts and substitution help!!

I'm sorry, but I simply cannot figure out what that integral is intended to be.

Is that [tex]\int_{-1}^0 e^{\sqrt{x+1}} dx[/tex] or [tex]\int_{-1}^0 e^{\sqrt{x}+ 1} dx[/tex] or [tex]\int_{-1}^0 e^{\sqrt{x}}+ 1 dx[/tex]?

If it is the first, take [itex]u= \sqrt{x+1}= (x+1)^{1/2}[/itex] so that [itex]du= (1/2)(x+1)^{-1/2}dx[/itex] so that [itex](x+1)^{1/2}du= u du= dx[/itex]. When x= -1, u= 0, when x= 0, u= 1 The integral becomes
[tex]\int_0^1 ue^{u}du[/tex]
and can be done by "integration by parts".

If the second, write it as [tex]e\int_{-1}^0 e^{\sqrt{x}}dx[/tex] and let [itex]u= \sqrt{x}[/itex].

If the third, write it as [tex]\int_{-1}^0 e^{\sqrt{x}}dx+ \int_{-1}^0 dx[/tex].
 
Last edited by a moderator:

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top