Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Evaluate the integral. $ \displaystyle \int^{…

02:22

Question

Answered step-by-step

Problem 37 Hard Difficulty

Evaluate the integral.

$ \displaystyle \int^{\pi/4}_{0} \frac{1 + \cos^2 \theta}{\cos^2 \theta} \,d\theta $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Joseph Russell
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Joseph Russell

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

00:35

Frank Lin

01:11

Amrita Bhasin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Related Topics

Integrals

Integration

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

05:53

Integrals - Intro

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

Video Thumbnail

40:35

Area Under Curves - Overview

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

Join Course
Recommended Videos

00:54

Evaluate the integral.
…

03:03

Evaluate the definite inte…

01:58

Evaluate the integral.
…

02:30

Evaluate the integral.

…

00:34

Evaluate the integral.
…

02:10

Evaluate $\int_{0}^{1} \ma…

01:10

Evaluate the following int…

05:05

Evaluate the integral.

…

01:12

Evaluate the integrals.

01:48

Evaluate the integrals
…

03:17

Evaluate the integral.

…

09:50

Evaluate the integral.
…

0:00

Find the definite integral…

0:00

How to evaluate this integ…

Watch More Solved Questions in Chapter 5

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74

Video Transcript

So here it might be helpful to split this term into. So we can write see pie. I can't write pie 54 So you can write first term as one over costa and squared fair plus Co sounds great of theater. Overcoat sounds great of data. So this is just the one and so one of the coast and square theater to. That's right. This first that will just be secret squared theater plus one again to put these parentheses. And so if we look to the table of indefinite air girls, we can see that sequence squared. Theta is just equal to the integral of secret squared. The theater will be tangent theater. So here what's right tangent theater A derivative of one will be theta. A profound pi over four. Lower bound of zero. It's not about you. Right? Tangent of pipe before Plus pi over four- Attention of zero plus zero. So tangent of pie before This will be one plus pi over four. My extension of 00 plus zero. Also zero. So he gets plus one plus pi over four.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
162
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
70
Hosted by: Alonso M
See More

Related Topics

Integrals

Integration

Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

05:53

Integrals - Intro

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

Video Thumbnail

40:35

Area Under Curves - Overview

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

Join Course
Recommended Videos

00:54

Evaluate the integral. $\int_{0}^{\pi / 4} \frac{1+\cos ^{2} \theta}{\cos ^{2}…

03:03

Evaluate the definite integral. $$ \int_{0}^{\pi / 4} \frac{1+\cos ^{2} \theta}…

01:58

Evaluate the integral. $$\int_{0}^{x / 4} \frac{1+\cos ^{2} \theta}{\cos ^{2} \…

02:30

Evaluate the integral. $ \displaystyle \int_0^{\frac{\pi}{2}} \cos^2 \theta …

00:34

Evaluate the integral. $$\int_{0}^{\frac{\pi}{4}} e^{\sin 2 \theta} \cos 2 \the…

02:10

Evaluate $\int_{0}^{1} \mathrm{dr} \int_{0}^{\pi / 4} r \cos ^{2} \theta \mathr…

01:10

Evaluate the following integrals. $$\int_{0}^{\pi / 2} \frac{\sin \theta}{1+\co…

05:05

Evaluate the integral. $ \displaystyle \int_0^{\frac{\pi}{4}} \sqrt{1 - \cos…

01:12

Evaluate the integrals. $\int_{0}^{\pi} \sqrt{1-\cos ^{2} \theta} d \theta$

01:48

Evaluate the integrals $$\int_{0}^{\pi} \sqrt{1-\cos ^{2} \theta} d \theta$$

03:17

Evaluate the integral. $ \displaystyle \int \frac{d \theta}{1 + \cos^2 \thet…

09:50

Evaluate the integral. $$\int_{0}^{\pi / 2} \sin ^{7} \theta \cos ^{5} \theta …

0:00

Find the definite integrals.

0:00

How to evaluate this integral?

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started