Help me please! Calculus - Theorem

Question

Find  

Options:

1. 
2. 
3. 
4. 

Answer 1

You are working with high-low=#2? This should be subtracted.

Answer 2

So you would think that this would just be sqrt(t²+1) but in this case we have something complicated as the limits of integration. Since the lower limit of integration is a constant and we are taking the derivative, we can ignore it (because the derivative of a constant is zero). So we just need to worry about the upper limit of integration.

We could plug in "4x" in place of "t" but the issue is "4x" has a derivative that is not equal to 1 so, by the chain rule, we must multiply by the derivative of "4x" which is 4.

So the answer becomes 4sqrt((4x)²+1) which is 4sqrt(16x² + 1) or answer 3