Function As Integral
Author: Doug Kuhlmann

Plot F(x)=Int(f(t)dt,a,b) for several values of a

a

x

Lower limit

Upper limit

Clear Traces

$ \begin {array} {l}
\text \bold {Instructions} \cr
\text {Adjust the lower limit slider to} \cr 
\text {the desired starting point.} \cr
\cr
\text {Use the \bold {Clear Traces}\ checkbox} \cr
\text {to erase extraneous traces.} \cr
\cr
\text {Then move or animate x to see the} \cr 
\text { graph of }

F\left( x \right) = \int\limits_a^x{f\left( t \right)dt}  \cr

\end {array} $

k(x) = 2 - x
h(x) = 1
g(x) = x
a = -5 (slider from -5 to 5, step 0.1)
f = Function(If[x < -1, g(x) + 2, If[x < 1, h, k]], -5, 5)
b = -5 (slider from a to 5, step 0.1)
Integ = Integral(f, a, b)
F: (b, Integ)
A: (a, 0)
B: (b, 0)
u = Vector(A, B)
text6: "x = " + b
d = false
text7: "$$
F\left( x \right) = \int\limits_a^x{f\left( t \right)dt}  = \int\limits_{" + (LaTeX[a]) + "}^{" + (LaTeX[b]) + "} {f\left( t \right)dt}  =  " + (LaTeX[Integ]) + "
$$"