The limits to this integration are -sqrt(2) and sqrt(2). The integration of y=-x^2 is the area (say A1) bounded by the curve and x axis. The integration of y=x^2-4 is the area (say A2) between the curve and x axis. If you have draw the graphs, you will see that the area between them is (A2-A1) Again A1 and A2 will be negative as they are below ... # Draw the curve in SVG ($x, $y) = (0, 0); $theta = pi / 2; $r = 4; for (split //, $peano) {if (/F/) {push @X, sprintf "%.0f", $x; push @Y, sprintf "%.0f", $y; $x += $r * cos ($theta); $y += $r * sin ($theta);} elsif (/\+/) {$theta += pi / 2;} elsif (/\-/) {$theta-= pi / 2;}} $max = max (@X, @Y); $xt =-min (@X) + 10; $yt =-min (@Y) + 10; $svg = SVG-> new (width => $max + 20, height => $max + 20);

Canvas offers two powerful features for drawing curves, quadraticCurveTo and bezierCurveTo. In the previous chapter, we have seen how to draw a line with Canvas. This is for a straight line, to draw a curve, two methods are offered. 1) The quadratic curve is a parabola, thus an arc, possibly asymmetric. I has only one inflection point. Draw a (yellow) circle and a fixed point P on the circle line. All circles that pass through the fixed point P and have their centres on the (yellow) circle have a cardioid as an envelope. Area and perimeter of the heart curve

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