Calculate Integral of -4f(x) from [0,1] using Graph | Step-by-Step Guide

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Homework Help Overview

The discussion revolves around calculating the integral of -4f(x) over the interval [0,1] using a provided graph. Participants are exploring the concept of integrals in relation to graphical representations of functions.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • The original poster expresses confusion about how to approach the integral with a graph, questioning what the problem is asking. Some participants suggest that the integral represents the area under the curve within the specified interval. Others propose using geometric formulas for area, such as the triangle area formula, while questioning the application of these concepts to the given function.

Discussion Status

Participants are actively engaging with the problem, offering hints and discussing different interpretations of the integral. There is a mix of attempts to apply geometric reasoning and numerical calculations, but no consensus has been reached on a correct method or solution.

Contextual Notes

Some participants are exploring integrals over different intervals, such as [0,7] and [0,8], indicating a broader context of area calculations involving various shapes, but there is uncertainty regarding the correctness of their approaches.

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Homework Statement


http://www.webassign.net/larson/4_03-48.gif

a) integral -4f(x) from [0,1] using that graph


Homework Equations





The Attempt at a Solution



i really have no idea what to do. i understand integrals but not with agraph? what is it asking me?
 
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Hint: An integral within an interval is the same as computing the area within that same interval.
 
so from [0,1] it is just 1/2bh? wouldn't that be just 1/2 x -4?
 
kings13 said:
so from [0,1] it is just 1/2bh? wouldn't that be just 1/2 x -4?

Numerically, the integral would be -1/2 since the height is at '-1'. So it would be -1/2*-4 I believe.
 
what about from [0,7] with the integral being 8f(x)dx
i did 1/2(7)(1+5)(8) which was wrong. what did i do wrong?
 
For [0,8] , you have

A triangle in [0,1]

a trapezium in [1,6]

a triangle in [6,8]

So you need to compute the areas there and add them up.
 

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