• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Integral Help

1. The problem statement, all variables and given/known data
As I was reviewing some of my previuosly learned calculus I came across somthing that I had either forgoten how to do or was never taught. How do you take the integral of somthing like this

[tex]\int \sqrt{\frac{9}{4}x+1}[/tex]

I don't know how to start with this one. Do I use U substitution?
 
First rewrite the integral as

dy=[tex]\int(\frac{9}{4x}+1)^{1/2}[/tex] dx

Now use the u substitution.

Thanks
Matt
 
Using U substitution I got ((9/4x+1)^1/2)/(27/8) I don't think I did this right.
 
I don't believe that is correct.

Try this.

Let u = [tex]\frac{9}{4x}[/tex]+1

Now find du/dx.
 
Du/dx is =36/16x[tex]^{2}[/tex]
 
Can you show your steps as to how you got that result please?
 
u=[tex]\frac{9}{4x}+1 [/tex]

[tex]\frac{0*4x-9*4}{(4x)^{2}}[/tex] So I made a mistake with the negative? The answer should be -36/16x^2.
 
Yes, you got it. Now perform the rest of the u substitution procedure and your done.
 
1. The problem statement, all variables and given/known data
As I was reviewing some of my previuosly learned calculus I came across somthing that I had either forgoten how to do or was never taught. How do you take the integral of somthing like this

[tex]\int \sqrt{\frac{9}{4}x+1}[/tex]

I don't know how to start with this one. Do I use U substitution?
I think the discussion got off track somewhere. The radicand above is [itex] \frac{9}{4}x+1[/itex] not [itex]\frac{9}{4x}+1[/itex]. Or was the original statement an error?

If the original is correct, then it can be easilly integrated by substitution - try [itex]u=\frac{9}{4}x+1[/itex].

(This looks like a Stewart's Calculus exercise.)

--Elucidus
 

Physics Forums Values

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