Assignment-10
Introduction
-The concept of upper sum and lower sum is commonly applied in calculating the area under a curve or area represented by a function or graph.
-we make approximation of the area of function by using rectangles.
-Upper sum The height of rectangles is absolute maximum of f(x) on the sub interval [A,B].
-Lower sum The height of rectangles is absolute minimum of f(x) on the sub interval [A,B].
Objectives
Dynamic applet of Lower and Upper sum of function f(x) with interval [A,B].
User guidelines
- you can see in this applet, a function with its lower sum and upper sum on the in the interval A,B].
- Here, upper sum denote the maximum area of the function f(x) between the interval [A,B] and lower sum denote the minimum area of the function f(x) between the interval [A,B].
- Now, move slider then you can see the number of rectangles n changes and upper sum,lower sum and difference of upper and lower sum also changes its values.
-So, if the number of rectangles n increases then upper sum is decrease ,lower sum increase and difference of upper and lower sum also decrease.
And if the number of rectangles n decrease then upper sum is increase ,lower sum decrease and difference of upper and lower sum is increases.
finally; conclude that, the upper sum and lower sum is depend on the number of rectangles we take and the interval we decide.
materials(Dynamic applet)
Test Your understanding
Q.n Change the number of rectangles n by using moving the slider with the mouse or move the slider then how does this affect the difference between lower and upper sum ?(drop your answer)
constructions Protocol
Construction steps of this applet are as follows:-
1.Enter a cubic polynomial f(x)=-0.5x3+2x2-x+1 by using input bar.
2.create two points A and B on the X-axis (which is interval of the function f(x)) by using point tool bar.
3.Create slider for the number n with interval 1 to 50 with increment 1.
4. Enter the Upper sum= upper sum[f,X(A),X(B),n] by using input bar.
here, X(A) gives the coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower sum and upper sum.
5.Enter lower sum= Lower sum[f,X(a),X(B),n].
6.Insert the dynamic text Upper sum = and select upper sum from the objects.
7.Insert the dynamic text Lower sum = and select lower sum from the objects.
8. calculate the Difference = Upper sum -Lower sum by using input bar.
9. Insert the dynamic text Difference = and select Difference from the objects.
10.Enter F- integral [f,X(A),X(B) by using input bar.
11.Insert dynamic text Integral- and select F from the objects .
At last, fix slider and decorate your applet by using object properties it helps to make applet more attractive and save your ggb file.