Area Between Curves
- Irina Boyadzhiev
- Area, Calculus, Definite Integral, Integral Calculus
Given are two functions f(x)=c(x-x1)(x-x2)(x-x3)(x-x4) and g(x)=0.6x+constant. We want to find the area surrounded by the two curves y=f(x) and y=g(x) and the vertical lines through a and b. You can study this problem by experimenting with different graphs. The area for each interval and the total area are calculated in the spreadsheet. The value of the definite integral of the difference f(x)-g(x) from a to b is given in cell B10 for comparison with the area between the curves. Drag the slider "Select Interval" to see the area in each interval. If f(x)>g(x), the area is colored in red; If f(x)<g(x), the area is colored in blue. Change f(x) by changing the coefficient c using the slider "f(x) coefficient" or by changing the x-intercepts of the function. ( To change the x-intercepts of f(x) click on "Show the x-intercepts of f(x)" and drag the blue points on the x-axis) Move the graph of g(x) up or down by dragging it.