Explanation Given: The integral function is, ∫ 0 π 4 6 tan 3 x d x . Formula used: Trigonometry identity, tan 2 x = ( − 1 + sec 2 x ) and integral formula, ∫ u n d u = u n + 1 n + 1 + c . Calculation: Consider the integral function, ∫ 0 π 4 6 tan 3 x d x Use the trigonometry identity, tan 2 x = ( − 1 + sec 2 x ) . Therefore, ∫ 0 π 4 6 tan 3 x d x = 6 ∫ 0 π 4 tan x ( sec 2 x − 1 ) d x Let u = sec x . d u = sec x tan x d x 1 u d u = tan x d x The function is written as, ∫ 0 π 4 6 tan 3 x d x = 6 ∫ 0 π 4 ( u 2 − 1 ) u d u = 6 ∫ 0 π 4 ( u − 1 u ) d u Apply an integral fo

Calculus: Early Transcendental Functions

7th Edition

ISBN: 9781337552516

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 8.3, Problem 61E

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To calculate: The definite integral ∫0π46tan3xdx.

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Chapter 8.3, Problem 60E

Chapter 8.3, Problem 62E

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Chapter 8 Solutions

Calculus: Early Transcendental Functions

Ch. 8.1 - CONCEPT CHECKS Integration Technique Describe how...Ch. 8.1 - CONCEPT CHECK Fitting Integrands to Basic...Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, selectthe...

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The definite integral ∫ 0 π 4 6 tan 3 x d x .

Solution Summary: The author explains how to calculate the definite integral underset_3(1-mathrmln2).

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To calculate: The definite integral ∫0π46tan3xdx.

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Chapter 8 Solutions