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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The graph of f consists of the three line segments shown. If g ( x ) = 0 x f ( t ) d t , find g(4) and g′(4).

Chapter 5, Problem 9RE, The graph of f consists of the three line segments shown. If g(x)=0xf(t)dt, find g(4) and g(4).

To determine

The value of the function g(4) and g(4).

Explanation

Given information:

The function as g(x)=0xf(t)dt.

The region lies between x=0 and x=5.

Draw the graph of f consists of the three line segments to find the area within the limit as shown  below in Figure 1.

Referto Figure (1).

Area of the shaded portion is separted by A1, A2, A3, A4 and A5.

Here, the area of the portion 1 is A1, the area of the portion 2 is A2, the area of the portion 3 is A3,the area of the portion 4 is A4 and the area of the portion 5 is A5.

The expression to find the value of g(4) isshown below:

g(x)=0xf(t)dt (1)

Substitute 4 for x in Equation (1).

g(4)=04f(t)dt=01f(t)dt

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