Thread: The fundamental theorem of calculus?

1. 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?

2. Re: The fundamental theorem of calculus?

Looks okay to me.

Whoops no, you're a factor of 2 out in the second term.

3. Re: The fundamental theorem of calculus?

What do you mean factor of 2 out in the second term?

4. Re: The fundamental theorem of calculus?

hi homeylova223

he means that you have lost the two from 2x^(-1/2)

5. Re: The fundamental theorem of calculus?

So would I be left with

(2/3)x^(3/2)-4x^(1/2) ?

6. Re: The fundamental theorem of calculus?

that is correct but don't forget the integration constant C.

7. Re: The fundamental theorem of calculus?

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.

8. Re: The fundamental theorem of calculus?

hi Prove It

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