## anonymous 3 years ago 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.

1. anonymous

$\int\limits_{1}^{3}(\frac{ d }{ dt }\sqrt{5+3t^4})dt$

2. zepdrix

Hmm so this is a little different than the last one. I think we have something like this going on.$\large \int\limits_1^3 \frac{d}{dt}f(t)dt \qquad = \qquad \int\limits_1^3 f'(t)dt \qquad = \qquad f(t)|_1^3$

3. zepdrix

$\large = f(3)-f(1)$ Make sense? :o

4. anonymous

yeah, you just took out the equation itself to understand the format

5. zepdrix

Yah these problems are always a little weird. We're differentiating, then anti-differentiating. So we end up with what we started with. Then we just evaluate it at the limits.

6. anonymous

then just go back and put the values into the function getting $\sqrt{248}-\sqrt{8}$ which is right Thanks, thats what I struggle with is where they want me to go with them

7. zepdrix

cool c: