You must post the calculations you have done
This is for an online practice quiz for participation points, but I'm not completely sure about my answer but I chose the option that was closest. Is this right?
Okay.. I just re-did my calculations because I didn't save them the first time. This time I got about 6. To do this I averaged the height of each trapezoid and the multiplied that by two (the width.) Do I need to type in each one I did? I know I'm wrong because it's too low. What am I doing wrong? I drew the trapezoids, added the two lengths/2*2 and added each of those individually and only got 6.
You didn't mention setting up the integral. It's not just the integral of the function - you need to calculate the arc length.
Each trapezoid is 1/4 wide, since there are eight of them and they span from x=0 to x=2. The exact value of the integral is about 13.965, so if you're getting 6, there's something wrong.
The attachment has a discussion of the trapezoid rule in general and your specific problem as an example. From the choice of answers given, the correct answer is c) 14.093. Your comment about computing the exact value of the integral is easier is a little suspect. Try computing the integral for the arc length; it's not that easy. Finally, if you Google "trapezoid rule calculator", you'll find a lot of sites that will do the arithmetic for you, and thus check your work.