Chapter 5: Integrals - Section 5.4 - The Fundamental Theorem of Calculus - Exercises 5.4 - Page 287: 63

$9$

let us consider $\dfrac{dc}{dx}=\dfrac{1}{2 \sqrt x}$ $\implies \dfrac{dc}{dx}=(\dfrac{1}{2} )x^{-(1/2)}$ $\implies c=(\dfrac{1}{2}) \int_0^{x} t dt$ $\implies [t^{(1/2)}]_0^{x}=\sqrt x$ Thus,we have $c(100)-c(1)=\sqrt {100}-\sqrt 1=9$