Evaluate the Integral

lovetolearn

New member
Joined
Mar 31, 2012
Messages
24
Is this the correct answer?


Evaluate the following integrals


1
∫ ((2x)/(sqrt1+2x))dx
0


ITG = (2/3)*(x-1)*sqrt(2x+1) + C

ITG(1) = 0
ITG(0) = -2/3
ITG(1) - ITG(0) = 2/3
--> 2/3
 
No, it isn't. Unfortunately, since you did not show how you did the integral, I cannot say how to correct it. Did you make the sustitution u= 1+ 2x?
 
I attached a picture of my work below. Thank you for looking over this problem. Where did I go wrong?
 

Attachments

  • work-1.jpg
    work-1.jpg
    26.3 KB · Views: 3
When you make the substitution \(\displaystyle u= v^2\), you have dv= 2udu but you have treated it as if it were du= 2vdv.

Instead, use the fact that \(\displaystyle \frac{u-1}{\sqrt{u}}= u^{1/2}- u^{-1/2}\).
 
Top