Concept explainers
Modify the computer program so that it will use ten trapezoids to approximate the area of the shaded region.RUN the program.
Compare your answer with that obtained when ten rectangles are used to compute the area of the shaded region.
Answer to Problem 3E
Answer by 10 trapezoid program is 0.334 , which is closer to actual area of shaded region
Answer by 10 rectangle program is 0.385
Explanation of Solution
Given:
The shaded region is bounded by the graph of
The program for computing and adding the areas of 5 trapezoids :
The program for calculating the area of shaded region using 10 rectangles :
Calculation:
A better approximation can be found by using 10 smaller trapezoids with base vertices at 0.0,0.1,0.2,…0.9,1.0 , and computing the sum of the areas of the 10 trapezoids.The parallel bases are vertical segments from the x -axis to the curve
The area of the shaded region is approximated by the sum of the areas of the 10 trapezoids.
The following comuter program will comute and add the areas of the 10 trapezoids .In line 30 and 40, B1 and B2 are the parallel bases of the trapezoid.In line 50, A gives the current total of all the areas.
If the program is run , the computer will print :
AREA IS APPROXIMATELY 0.334
RUN the program for calculating the area of shaded region using 10 rectangles :
If the program is run , the computer will print:
AREA IS APPROXIMATELY 0.385
The actual area of the shaded region is
So, clearly , the computer program that calculates the area of the shaded region via 10 trapezoids is approximately closer to the actual answer.
Chapter 11 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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