Graph the functions in Exercises 11–16 and

Chapter , Problem 16AAE

(choose chapter or problem)

The Fundamental Theorem applies to piecewise continuous functions with the restriction that \((d / d x) \int_{a}^{x} f(t) d t\) is expected to equal \(f(x)\) only at values of \(x\) at which \(f\) is continuous. There is a similar restriction on Leibniz’s Rule (see Exercises 31–38).

Graph the functions in Exercises 11–16 and integrate them over their domains.

                  \(h(r)=\left\{\begin{array}{lrl}r, & -1 & \leq r<0 \\1-r^{2}, & 0 & \leq r<1 \\1, & 1 & \leq r \leq 2\end{array}\right.\)

Equation Transcription:

{

Text Transcription:

(d/dx) integral_a ^x f(t)dt

f(x)

x

f

h(r)={_1,1 leq  r leq 2 ^1-r^2, 0 leq r < 1 ^r,  -1  leq r < 0