Question

let h(x)=integral of 0 to x f(t)dt
Find h(3), h'(3), and h"(3)

Answer 1

Hmm this is a neat problem :)
Fundamental Theorem of Calculus.

Answer 2

\[h(x)=\int\limits_{0}^{x} f(t)dt \]

Answer 3

We simply use FTC, Part 2 for the first part,\[h(3)=\int\limits\limits_{0}^{3} f(t)dt=F(t)|_0^3\]

Answer 4

=F(3)-F(0)
right? :)

Answer 5

Were you given a function for f? :d

Answer 6

Graphically, what does \( \int_0^3 f(x) dx \) represent?