Let F of x equals the integral from x to 1 of the square root of the quantity of 1 plus t squared . Use your calculator to find F'(1)

Question

Let  . Use your calculator to find F'(1).

a	0
b
c
d	1

my answer is c

Answer 1

F(x) = ∫_{(from x to 1)} √(1+t²)dt = -∫_{(from 1 to x)} √(1 + t²)dt

By the Fundamental Theorem of Calculus, F'(x) = -√(1 + x²).

So, F'(1) = -√(1 + 1²) = -√2.