Question

What's the best way to integrate this question and how do you do it?

Answer 1

https://secure-media.collegeboard.org/apc/ap03_sg_calculus_bc_26477.pdf
Question 3 was a question I got on my calc test. It asked to set up and find the integral of this area WITHOUT a calculator. I set up the integral, but I have no idea how to integrate \[\sqrt{1+y ^{2}}\]
I hear trig sub, IBP, and geometry are methods to go about this, but I'm not entirely sure what is best. I'm leaning towards trig sub, as geometry and IBP are pretty complex to think about conceptually for me, but I don't completely understand it. All I know is that you would replace the y^2 with tan^2x, making it the sqrt of sec^2x, but that's about it.

Answer 2

Hey @InsatiableSuffering, are you sure this is noncalculator? I honestly couldn't figure out a way either w/o calculator, but I looked up the FRQ and it seems like it's calc-OK based on this video -
https://www.youtube.com/watch?v=Hk2Wi_k_JCs

Answer 3

Well, our teacher gave us a calculator portion of the test at the beginning of class, and I looked around the end of class, and absolutely nobody was using one for the very last frq. I am 100% certain that this can be solved without a calculator, but I'm not sure how.

Answer 4

I used symbolab to integrate it, but I got really confused. It might actually work, not completely sure though.

Answer 5

Everybody actually asked the same question at the end of class; how do you integrate sqrt1+y^2?

Answer 6

It looks like the right side of a hyperbola but I'm not sure if there's a way to find area through that. I've had questions involving such integrands yet I don't bother but plug in the calculator lol.