Chapter 13.1, Problem 26E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

Use the function
*left-hand* endpoint of each subinterval for Problems 26 and 27.

What is the area of the

(a) first rectangle?

(b) second rectangle?

(c) *i*th rectangle?

**(a)**

To determine

**To calculate:** The area of the first rectangle under the curve of the function *n* equal subintervals where the function is evaluated at left end points of each subinterval.

Explanation

**Given Information:**

The curve is *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 *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

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

**Calculation:**

The curve is *n* subintervals and the function is evaluated at left end points of the subintervals.

The base of the rectangles to approximate the area is *n* subintervals.

Since, the function is defined from

**(b)**

To determine

**To calculate:** The area of the second rectangle under the curve of the function *n* equal subintervals where the function is evaluated at left end points of each subinterval.

**(c)**

To determine

**To calculate:** The area of the *n* equal subintervals where the function is evaluated at left end points of each subinterval.

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