   Chapter 4.3, Problem 53E

Chapter
Section
Textbook Problem

EXPLORING CONCEPTSApproximation In Exercises 53 and 54, determine which best approximates the definite integral. Make your selection on the basis of a sketch. ∫ 0 4 x   d x 5-31028

To determine

To calculate: The approximate value of the integral 04xdx. By the use of sketch of the expression.

Explanation

Given: The integral is,

04xdx

With the provided options,

(a)5

(b) 3

(c) 10

(d)2

(e) 8

Formula used: We know that area bounded by the graph of f(x) and x -axis on interval [a,b] is represented by,

abf(x)dx

Calculation: We will draw the rough sketch of the provided function f(x)=x break the interval [0,4].

Into four equal parts each of equal width is,

404=1.

On substitution x=0,1,2,3,4 and find out value of the function at these values of x.

Put x=0 to get,

f(0)=0=0

Put x=1 to get,

f(1)=1=1

Put x=2 to get,

f(2)=21.4

Put x=3 to get,

f(3)=31

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