   Chapter 4.3, Problem 47E

Chapter
Section
Textbook Problem

Think About It The graph of f consists of line segments and a semicircle, as shown in the figure. Evaluate each definite integral by using geometric formulas. (a) ∫ 0 2 f ( x ) d x (b) ∫ 0 6 f ( x ) d x (c) ∫ − 4 2 f ( x ) d x (d) ∫ − 4 6 f ( x ) d x (e) ∫ − 4 6 | f ( x ) | d x (f) ∫ − 4 6 [ f ( x ) + 2 ] d x

(a)

To determine

To calculate: The integral 02f(x)dx using the graph.

Explanation

Given:

The graph of f consists of line segments and a semicircle

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. Then,

Area=abf(x)dx

Calculation:

The integral 02f(x)dx

(b)

To determine

To calculate: The integral 26f(x)dx using the graph.

(c)

To determine

To calculate: The integral 42f(x)dx using the graph.

(d)

To determine
The integral 46f(x)dx using the graph.

(e)

To determine

To calculate: The integral 46|f(x)|dx using the graph.

(f)

To determine

To calculate: The integral 46[f(x)+2]dx using the graph.

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