Here is a link to my previous question Question about plotting a curve and tangent lines
I want to know how can the area be found between the curve and tangent line for between Point Fun1 and Fun2.This is what I did but im not sure its correct or not. Do I have to use piecewise integration?
Clear[f, x, g]
f[x_] = x^3
g = f[1.2] + f'[1.2] (x - 1.2)
Plot[{f[x], g}, {x, -5, 5}, PlotRange -> 20]
NIntegrate[f[x], {x, -2.4, 1.4}]
NIntegrate[f[x], {x, -2.4, 4.8}]
I also want to know how can I make the Manipulate function work for moving the point Fun1 to 15 positions in the interval[-5,0). I also want to learn how can I use the Manipulate function to update the drawing each time the points move(the drawing shows the tangents the intersection points)
Manipulate[
Plot[{f[x],l[x]}, {t, -x, x}, Filling -> Axis,
PlotRange -> {{-5, 10}, {-5, 10}}, N[Erf[x]]], {1.3, 0.5}]], {x,
0.0001, 3}]