Learning Guide Learning Guide

226 • Chapter 6: Examples from Calculus∫ 1+ sin(x) dx2> value( % );12 x − cos(x)Define the function F to be the antiderivative.> F := unapply( %, x );F := x → 1 2 x − cos(x)Choose the constant of integration so that F (0) = 0.> F(x) - F(0);12 x − cos(x) + 1> F := unapply( %, x );F := x → 1 2 x − cos(x) + 1If you plot F and the left-boxes together, you can see that F increasesmore when the corresponding box is larger.> with(plots):> display( [ plot( F(x), x=0..10, color=blue, legend="F(x)" ),> ApproximateInt( f(x), x=0..10, partition=14,> method=left, output=plot) ] );