Final Exam S07 Design• Problem on Areas Between Curves> restart;> with(plots):Warning, the name changecoords has been redefined > f:=x->1+sqrt(x); := f → x + 1x> g:=x->3-x; := g → x − 3 x> h:=x->x^2/2; := h → x12x2> plot([f(x),g(x),h(x)],x=0..2.5,y=0..3.5,scaling=constrained, color=[red,green,blue],thickness=4);> pf:=plot(f(x),x=0..2.5,y=0..3,color=black,thickness=4, labelfont=[TIMES,ITALIC,18], axesfont=[TIMES,ROMAN,16]):> ptf:=textplot([0.4,1.9,`f(x)`],font=[TIMES,ROMAN,18]):> pg:=plot(g(x),x=0..2.5,y=0..3,color=black,thickness=4):> ptg:=textplot([1.5,1.9,`g(x)`],font=[TIMES,ROMAN,18]):> ph:=plot(h(x),x=0..2.5,y=0..3,color=black,thickness=4):> pth:=textplot([1.3,0.4,`h(x)`],font=[TIMES,ROMAN,18]):> fg:=x->min(f(x),g(x)); := fg → x ()min ,()f x ()g x> pfg:=plot(fg(x),x=0..2.5,color=grey,filled):> phf:=plot(h(x),x=0..2.5,color=white,filled):> > display([pf,ptf,pg,ptg,ph,pth,phf,pfg]);> c1:=solve(f(x)=g(x),x); := c1 1> c2:=solve(g(x)=h(x),x)[2]; := c2− + 1 7> evalf(c1);evalf(c2);1.1.645751311> J1:=Int(g(x)-f(x),x=0..c1); := J1 d⌠⌡⎮⎮01 − − 2 x xx> J2:=Int(g(x)-h(x),x=c1..c2); := J2 d⌠⌡⎮⎮⎮⎮1− + 17 − − 3 x12x2x> J:=simplify(value(J1+J2)); := J − + 2967 73> evalf(J);1.340086392> eqn:=simplify(g(x)-h(x)); := eqn − − 3x12x2> solve(eqn=0,x);,− − 1 7 − + 1 7> > > >
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