Use the following functions defined in the GraphicsFunctions.mthZG4ZTI utility file to plot areas associated with graphs of functions of a single variable in a 2D-plot window.  Note that by interchanging the roles of x and y in these functions, the area plots can be carried out with respect to the y-axis as the basis, instead of the x-axis. 


AreaUnderCurve(u, x, a, b, y) plots the area under the graph of the function y = u(x) and above the x-axis from x = a to b (a < b).  For example, to plot the area under the function y = x + cos(x) from x = 0 to 3, plot the expression

AreaUnderCurve(x + COS(x), x, 0, 3, y)


AreaUnderCurve(u, y, a, b, x) plots the area to the left of the graph of the function x = u(y) and to the right of the y-axis from y = a to b (a < b).  For example, to plot the area to the left of the function x = y + cos(y) from y = 0 to 3, plot the expression

AreaUnderCurve(y + COS(y), y, 0, 3, x)


AreaOverCurve(u, x, a, b, y) plots the area over the graph of the function y = u(x) and under the x-axis from x = a to b (a < b).  For example, to plot the area over the function y = sin(x) - x from x = 1 to 3, plot the expression

AreaOverCurve(SIN(x) - x, x, 1, 3, y)


AreaOverCurve(u, y, a, b, x) plots the area to the right of the graph of the function x = u(y) and to the left of the y-axis from y = a to b (a < b).  For example, to plot the area to the right of the function x = sin(y) - y from y = 1 to 3, plot the expression

AreaOverCurve(SIN(y) - y, y, 1, 3, x)


AreaBetweenCurves(u, v, x, a, b, y) plots the area between the graphs of the functions y = u(x) and y = v(x) from x = a to b (a < b).  For example, to plot the area between the functions y = sin(2·x) and y = cos(3·x) from x = -π to π, plot the expression

AreaBetweenCurves(SIN(2·x), COS(3·x), x, -pi, pi, y)


AreaBetweenCurves(u, v, y, a, b, x) plots the area between the graphs of the functions x = u(y) and x = v(y) from y = a to b (a < b).  For example, to plot the area between the functions x = sin(2y) and x = cos(3·y) from y = -π to π, plot the expression

AreaBetweenCurves(SIN(2·y), COS(3·y), y, -pi, pi, x)


By letting v = 0, AreaBetweenCurves can also be used to plot the area associated with the definite integral of y = u(x)  from x = a to b (a < b) in a single color.  For example, to plot the integral of the function y = sin(2·x) + cos(3·x) from x = -π to π, plot the expression 

AreaBetweenCurves(SIN(2·x) + COS(3·x), 0, x, -pi, pi, y)


PlotInt(u, x, a, b, y) plots the area associated with the definite integral of the function y = u(x) from x = a to b.  For PlotInt, use rectangular coordinates and have the 2D-plot window's Options > Approximate Before Plotting optionEVZ132 turned on.  For example, to plot the integral of the function y = x + sin(2·x)  from x = -3 to 3, plot the expression

PlotInt(x + SIN(2·x), x, -3, 3, y)


PlotInt(u, y, a ,b, x) plots the area associated with the definite integral of the function x = u(y) from y = a to b.  For example, to plot the integral of the function x = y + sin(2·y)  from y = -3 to 3, plot the expression

PlotInt(y + SIN(2·y), y, -3, 3, x)


If the option to automatically change plot colors is on (see Options > Display > Color commandJDDXSP), the positive part of the integral is plotted in one color, then the negative part is plotted in a contrasting color.  For example, compare the previous plot with a plot of the expression

PlotInt(x + SIN(2·x), x, 3, -3, y)


Many other examples of plotting and filling the areas of curves can be constructed directly using Boolean plots.  For example, to plot and fill a circle of radius 2 with center at (1,2), plot the expression

(x-1)^2 + (y-2)^2 = 4 OR (x-1)^2 + (y-2)^2 <= 4


If the plot looks like an ellipse, use the Set > Aspect Ratio command02_MF4 to make it a true circle.  As another example, to plot the area between x = y² and x = sin(y) for y = -2 to 2, plot the expression

x=y^2 OR x=SIN(y) OR ((x-y^2)·(SIN(y)-x) >= 0 AND -2 <= y <= 2)


Other Graphics FunctionsZG4ZTI 

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