   Chapter 5, Problem 2RCC ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) Write the definition of the definite integral of a continuous function from a to b.(b) What is the geometric interpretation of ∫ a b f ( x )   d x if f(x) ≥ 0?(c) What is the geometric interpretation of ∫ a b f ( x )   d x if f(x) takes on both positive and negative values ? Illustrate with a diagram.

(a)

To determine

To write: The definition for the definite integral of a continuous function from a to b.

Explanation

Consider the function f which is continuous on interval [a,b].

Divide the interval into n subintervals of equal width, Δx=ban.

Let x0(=a),x1,x2,....,xn(=b) be the end and intermediate points of the subintervals.

Then, the definite interval is the sum of the area of the subintervals

(b)

To determine

To find: The geometric interpretation of abf(x)dx if f(x)0.

(c)

To determine

To find: The geometric interpretation of abf(x)dx, if f(x) have both positive and negative values.

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