# Thread: Fundamental Theorem of Calc. Integration

1. ## Fundamental Theorem of Calc. Integration

Evaluate the definite integral
using the Fundamental Theorem of Calculus. You will need accuracy to at least 4 decimal places for your numerical answer to be accepted. You can also leave your answer as an algebraic expression involving square roots.

I understand the FTC when you have x in the limits but since there is no x I'm confused on how to solve this.
Thanks!

2. Originally Posted by Casas4
Evaluate the definite integral
using the Fundamental Theorem of Calculus. You will need accuracy to at least 4 decimal places for your numerical answer to be accepted. You can also leave your answer as an algebraic expression involving square roots.

I understand the FTC when you have x in the limits but since there is no x I'm confused on how to solve this.
Thanks!
$\displaystyle I=\sqrt{2+3t^4}+C$
$\displaystyle I=\sqrt {2+3\times 6^4} - \sqrt {2+3\times 5^4}$

3. Originally Posted by Casas4
Evaluate the definite integral
using the Fundamental Theorem of Calculus. You will need accuracy to at least 4 decimal places for your numerical answer to be accepted. You can also leave your answer as an algebraic expression involving square roots.

I understand the FTC when you have x in the limits but since there is no x I'm confused on how to solve this.
Thanks!
$\displaystyle \int_5^6 \frac{6t^3}{\sqrt{2+3t^4}} \, dt = \left[\sqrt{2+3t^4}\right]_5^6$