   Chapter 4.3, Problem 54E

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 1 / 2 4 cos π x   d x 4 4 3 16 2 π − 6

To determine

To calculate: The approximate value of the integral 0124cosπxdx by the sketch of the expression from the provided options

(a) 4

(b) 43

(c) 16

(d) 2π

(e) 6

Explanation

Given: The integral is,

0124cosπxdx

With the provided options,

(a) 4

(b) 43

(c) 16

(d) 2π

(e) 6

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

abf(x)dx

Calculation: we will draw the rough sketch of the provided function f(x)=4cosπx break the interval [0,12] into two equal parts each of width 14.

On substitution x=0,14,12 and find out value of the function at these values of x.

Put x=0,

f(0)=4cosπ×0=4cos0=4(1)=4

Put x=14,

f(14)=4cos(π4)=42=22

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