   Chapter 4, Problem 20PS

Chapter
Section
Textbook Problem

Minimizing an Integral Determine the limits of integration where a ≤ b such that ∫ a b ( x 2 − 16 ) d x has minimal value

To determine

To calculate: The values of a and b that lead to the definite integral ab(x216)dx having a minimum value.

Explanation

Given:

The definite integral ab(x216)dx.

Formula Used:

The area below the curve y=f(x) and above the x-axis when x lies in the interval [a,b] is given by:

A=abf(x)dx

Calculation:

Consider the function in the integrand.

y=x216(y(16))=(x0)2

This is the equation of a parabola that open upwards and has a vertex at point (0,16)

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