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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

The graph of f is shown. Evaluate each integral by interpreting it in terms of areas.

(a) 0 2 f ( x ) d x

(b) 0 5 f ( x ) d x

(c) 5 7 f ( x ) d x

(d) 0 9 f ( x ) d x

Chapter 4.2, Problem 33E, The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. a 02f(x)dx b

To determine

a)

To evaluate:

The given integral by interpreting it in terms of  thearea.

Explanation

Concept:

A definite integral can be interpreted as a net area, that is, difference of the areas abf(x)dx=A1-A2

where A1 is the area of region above x- axis and below the graph of f, and A2 is the area of region below x- axis and above the graph of f.

Given:

02f(x)dx

Calculations:

To find the area under the curve, from the points 0 to 2, means to calculate the area of the shaded region as shown in the figure below.

From the graph, A1 is the area of atrapezoid

To determine

b)

To evaluate:

The given integral by interpreting it in terms of area

To determine

c)

To evaluate:

The given integral by interpreting it in terms of area.

To determine

d)

To evaluate:

The given integral by interpreting it in terms of area.

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