   Chapter 4.3, Problem 48E

Chapter
Section
Textbook Problem

Think About It The graph of f consists of line segments, as shown in the figure. Evaluate each definite integral by using geometric formulas. (a) ∫ 0 1 − f ( x ) d x (b) ∫ 3 4 3 f ( x ) d x (c) ∫ 0 7 f ( x ) d x (d) ∫ 5 11 f ( x ) d x (e) ∫ 0 11 f ( x ) d x (f) ∫ 4 10 f ( x ) d x

(a)

To determine

To calculate: The integral 01f(x)dx using the given graph; Explanation

Given:

The graph of f consists of line segments is:

Formula used:

If f is continuous and non-negative on the closed interval [a,b] then the area of the region bounded by the graph of f, the x-axis and the vertical lines x=a,x=b that depict the border points is

Area=abf(x)dx

Calculation:

From the given graph, the integral 01f(x)dx is area of triangle with base 1unit and height 1 unit

(b)

To determine

To calculate: The integral 343f(x)dx using the given graph.

(c)

To determine
The integral 07f(x)dx using the given graph.

(d)

To determine

To calculate: The integral 511f(x)dx using the given graph.

(e)

To determine
The integral 011f(x)dx using the given graph.

(f)

To determine
The integral 410f(x)dx using the given graph.

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