Question attached to image 12:13 PM Tue Dec 154%Evuluute3 secce) ( sede) t tano)o=do-(include all steps)7

Name: Question attached to image 12:13 PM Tue Dec 154%Evuluute3 secce) ( sed
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Description: Question attached to image 12:13 PM Tue Dec 154%Evuluute3 secce) ( sede) t tano)o=do-(include all steps)7

To Determine: evaluate ∫0π43secθsecθ+tanθdθ Given: we have an integral ∫0π43secθsecθ+tanθdθ…

Answered: S. Evaluute 3 seale) ( sede) +…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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3 secce) ( sede) t tano)o=
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7

Expert Solution

Step 1

To Determine: evaluate $\int_{0}^{\frac{π}{4}} 3 s e c θ (s e c θ + \tan θ) d θ$

Given: we have an integral $\int_{0}^{\frac{π}{4}} 3 s e c θ (s e c θ + \tan θ) d θ$

Explanation: now we have an integral

$\int_{0}^{\frac{π}{4}} 3 s e c θ (s e c θ + \tan θ) d θ$

taking 3 common outside the integral .

$= 3 \int_{0}^{\frac{π}{4}} (s e c^{2} θ + s e c θ \tan θ) d θ = 3 \int_{0}^{\frac{π}{4}} (\frac{1}{\cos^{2} θ} + \frac{\tan θ}{\cos θ}) d θ = 3 (\int_{0}^{\frac{π}{4}} \frac{1}{\cos^{2} θ} d θ + \int_{0}^{\frac{π}{4}} \frac{\tan θ}{\cos θ} d θ)$

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