   Chapter 5.2, Problem 61E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Use Property 8 to estimate the value of the integral. ∫ π / 4 π / 3 tan x   d x

To determine

To calculate: The value of the integral function π4π3tanxdx.

Explanation

Given information:

The integral function is π4π3tanxdx (1)

Consider the function f(x)=tanx (2)

The region lies between x=π4 and x=π3.

Apply property 8 of integrals:

If mf(x)M for axb, then m(ba)abf(x)dxM(ba).

To find the absolute maximum value M as shown below:

Calculate absolute maximum value using Equation (2).

M=f(x) (3)

Substitute π3 for x in Equation (3).

M=f(π3)=tan(π3)=3

To find the absolute minimum value m as shown below:

Calculate absolute minimum value using Equation (2).

m=f(x) (4)

Substitute π4 for x in Equation (4)

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