Graph the functions in Exercises 11–16 and

Chapter , Problem 15AAE

(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.

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

Equation Transcription:

{

Text Transcription:

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

f(x)

x

f

f(x)={_2,1 leq  x leq 2 ^1-x2, -1 leq x < 1 ^1,  -2  leq x < -1