   Chapter 13.1, Problem 26E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Use the function y   =   2 x  from  x =  0  t o   x =   1   a n d   n equal subintervals with the function evaluated at the left-hand endpoint of each subinterval for Problems 26 and 27.What is the area of the(a) first rectangle?(b) second rectangle?(c) ith rectangle?

(a)

To determine

To calculate: The area of the first rectangle under the curve of the function y=2x from x=0 to x=1 and n equal subintervals where the function is evaluated at left end points of each subinterval.

Explanation

Given Information:

The curve is y=2x from x=0 to x=1 and the interval [0,1] is divided into n subintervals and the function is evaluated at left end points of the subintervals.

Formula used:

The base of the rectangles to approximate the area is ban where the interval [a,b] on which function is defined is divided into n subintervals.

The height of the rectangles is the value of the function calculated at the left end point of the interval containing the base.

The area of a rectangle is base×height.

The approximated area under the curve is sum of the areas of each rectangle.

Calculation:

The curve is y=2x from x=0 to x=1 and the interval [0,1] is divided into n subintervals and the function is evaluated at left end points of the subintervals.

The base of the rectangles to approximate the area is ban where the interval [a,b] on which function is defined is divided into n subintervals.

Since, the function is defined from x=0 to x=1. So, a=0 and b=1

(b)

To determine

To calculate: The area of the second rectangle under the curve of the function y=2x from x=0 to x=1 and n equal subintervals where the function is evaluated at left end points of each subinterval.

(c)

To determine

To calculate: The area of the ith rectangle under the curve of the function y=2x from x=0 to x=1 and n equal subintervals where the function is evaluated at left end points of each subinterval.

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