91Ó°ÊÓ

The shaded region is bounded by the graph of$y=x^2$, by the x-axis , and by the vertical line through the points$(1,0)$and$(1,1)$.

The program for calculating the area of shaded region using 10 rectangles :$\begin{array}{l}10\text{LET}X=0.1\\ 20\text{FOR}N=1\text{TO10}\\ \text{30LET}Y=X↑2\\ 40\text{LET}A=A+Y*0.1\\ 50\text{LET}X=X+0.1\\ 60\text{NEXT}N\\ 70\text{PRINT"AREAISAPPROXIMATELY";}A\\ 80\text{END}\end{array}$

We can approximate the area of the shaded region by drawing 100 rectangles having base vertices at$x=0,0.01,0.02,0.03,…,1.00,$and computing the sum of the areas of the 100 rectangles. The base of each rectangle is$0.01$, and the height of each rectangle is given by$y=x^2$

The following comuter program will comute and add the areas of the 100 rectangles .In line$30,Y$is the height of each rectangle.In line 40 , A gives the current total of all the areas.

$\begin{array}{l}10\text{LET}X=0.01\\ 20\text{FOR}N=1\text{TO100}\\ \text{30LET}Y=X↑2\\ 40\text{LET}A=A+Y*0.01\\ 50\text{LET}X=X+0.01\\ 60\text{NEXT}N\\ 70\text{PRINT"AREAISAPPROXIMATELY";}A\\ 80\text{END}\end{array}$

Therefore, If the program is run, the computer will print AREA IS APPROXIAMTELY $0.33835$