Question

I'm tired I feel like I missing something...

Find the derivative..
h '(x) = sqrt(5+t^2)

Answer 1

Sorry, evaluated at [x^2 + 1, 2]

Answer 2

Pretty sure you meant to say, find the derivative:
\[\frac{d}{dx}\int_2^{x^2+1}\sqrt{5+t^2}~dt\]
This involves the use of the first fundamental theorem, which says
\[\frac{d}{dx}\int_c^{g(x)}f(t)~dt=f(g(x))\cdot g'(x)\]
Identify your \(f\) and \(g\), and do the necessary computations.

Answer 3

@sithandgiggles you were almost correct in your assumption. The integral you have presented is the negative version, so is that the first step?

Answer 4

Oh you meant the interval starts at \(x^2+1\) and ends at 2? Okay, yes, I have the negative of what you need.

So yeah, you should have \(-f(g(x))\cdot g(x)\).