# The fundamental theorem of calculus?

• Aug 14th 2011, 10:56 AM
homeylova223
The fundamental theorem of calculus?
Evaluate the definite integral

from x=1 to x=4

((x-2))/((square root x)) This is what I did

x^(1/2)-(x)^(-1/2)

(2/3)x^(3/2)-2x^(1/2)

Did I set this up correctly?
• Aug 14th 2011, 10:58 AM
Matt Westwood
Re: The fundamental theorem of calculus?
Looks okay to me.

Whoops no, you're a factor of 2 out in the second term.
• Aug 14th 2011, 11:02 AM
homeylova223
Re: The fundamental theorem of calculus?
What do you mean factor of 2 out in the second term?
• Aug 14th 2011, 11:06 AM
anonimnystefy
Re: The fundamental theorem of calculus?
hi homeylova223

he means that you have lost the two from 2x^(-1/2)
• Aug 14th 2011, 11:11 AM
homeylova223
Re: The fundamental theorem of calculus?
So would I be left with

(2/3)x^(3/2)-4x^(1/2) ?
• Aug 14th 2011, 11:15 AM
anonimnystefy
Re: The fundamental theorem of calculus?
that is correct but don't forget the integration constant C.
• Aug 14th 2011, 05:26 PM
Prove It
Re: The fundamental theorem of calculus?
Quote:

Originally Posted by anonimnystefy
that is correct but don't forget the integration constant C.

It's a definite integral, so the C isn't needed. Instead the OP needs to find the difference between the integral value when it is evaluated at the upper and lower terminals.
• Aug 15th 2011, 02:57 AM
anonimnystefy
Re: The fundamental theorem of calculus?
hi Prove It

sorry i didn't see that it was a definite integral.my mistake.