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_0^…

05:05

Question

Answered step-by-step

Problem 45 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int_0^{\frac{\pi}{6}} \sqrt{1 + \cos 2x} dx $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

JH
J Hardin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by J Hardin

Numerade Educator

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

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Related Topics

Integration Techniques

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
Recommended Videos

01:24

Evaluate the integral.
…

06:01

Evaluate the integrals.

02:43

Evaluate the integral.

…

00:53

Evaluate the definite inte…

04:02

Evaluate the integrals.

02:50

Evaluate the integrals
…

01:29

Evaluate the integral.

…

01:39

Evaluate the definite inte…

05:15

Evaluate the integrals
…

03:59

Evaluate the integral.
…

Watch More Solved Questions in Chapter 7

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

Video Transcript

this problem is from Chapter seven section to a problem. Number forty five in the book Calculus Early Transcendental lt's a Condition by James Store. We hear we have a definite integral of the square of one plus coast high to X. So here let's talk about co sign of two X. We can use a double ankle formula to rewrite this as two times co sign squared X minus one. Then from here we have one plus coastline to X. Here we can cancel the ones and we just have to co sign Squared X. Then we could take the square root so we can write. This is I want to times the square room of Coastline Square, which isn't necessarily co sign because technically, the square root of the square is going to be the absolute value. So this case, we should to be safe. You should always write absolute value there, I guess in general, the rule that I'm using here is squirt of a square is absolute value in our problem. However, this will be actually will simplify too, two times called radical two times co sign since coastline eggs. It's positive in our inseparable of the liberation. What that said we can rewrite are integral. That becomes zero time for six time's radical, too times cosine x so you can pull out the rat radical to outside the integral if you like. So Integral co sign a sign so they get radical, too time. Sinus evaluated at zero and pi over six. So sign of viruses. One half and sign of zero zero So we get squared or two divided by two, and that's our answer.

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
177
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
75
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
Recommended Videos

01:24

Evaluate the integral. $\int_{0}^{\pi / 6} \sqrt{1+\cos 2 x} d x$

06:01

Evaluate the integrals. $\int_{0}^{\pi / 6} \sqrt{1+\sin x} d x$

02:43

Evaluate the integral. $ \displaystyle \int_0^{\frac{1}{2}} x \cos \pi x dx $

00:53

Evaluate the definite integral. $\int_{0}^{\sqrt{\pi}} x \cos \left(x^{2}\rig…

04:02

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

02:50

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

01:29

Evaluate the integral. $ \displaystyle \int_0^\pi \sin 6x \cos 3x\ dx $

01:39

Evaluate the definite integral. $$\int_{0}^{\pi^{2}} \frac{\cos \sqrt{x}}{\sqrt…

05:15

Evaluate the integrals $$\begin{aligned}&\int_{0}^{\pi / 6} \sqrt{1+\sin x} d x…

03:59

Evaluate the integral. $$ \int_{0}^{\pi} \sin 6 x \cos 3 x d x $$
Additional Mathematics Questions

01:27

Use the Distributive Property to remove the parentheses.
$$
(x-4)(x-2)…

00:46

True or False $\sqrt[5]{-32}=-2$

01:12

True or False $\sqrt[4]{(-3)^{4}}=-3$

01:54

Write each number in scientific notation.
$$
32,155
$$

01:03

Explain why $\frac{4+3}{2+5}$ is not equal to $\frac{4}{2}+\frac{3}{5}$

01:08

Write each number as a decimal.
$$
9.7 \times 10^{3}
$$

00:48

Write each number as a decimal.
$$
9.88 \times 10^{-4}
$$

01:11

If $2=x,$ why does $x=2 ?$

01:03

If $x=5,$ why does $x^{2}+x=30 ?$

01:19

Write each number as a decimal.
$$
1.1 \times 10^{8}
$$

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