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 \f…

07:59

Question

Answered step-by-step

Problem 17 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{x}{\sqrt{x^2 - 7}}\ 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 3

Trigonometric Substitution

Related Topics

Integration Techniques

Discussion

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

Missouri State University

Anna Marie Vagnozzi

Campbell 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

01:10

Evaluate the integral.
…

03:02

Evaluate the integral.
…

02:58

Evaluate the integral by s…

03:10

Use a substitution to eval…

02:14

Evaluate the integral.
…

01:05

Evaluate the following int…

01:17

Evaluate the definite inte…

02:04

Evaluate.
$$\int_{0}^{\…

02:09

Evaluate the integral.
…

01:02

Evaluate the definite inte…

01:07

Evaluate the definite inte…

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

Video Transcript

let's evaluate the integral of X over the square root of X squared minus seven. So, looking in the denominator, we see an X squared minus seven, which is an expression of the form X squared, minus a square. And we know that in this situation the substitution to use is X equals a seek and data. Now, since a square to seven that tells us that we could take a to be the square root of seven. So our trick some should be X equals square root of seven c can data and taking the differential on each side. This gives us the X equals Route seven c can't time standard. So let's go ahead and plug in the stuff into the new integral. Also, maybe we should, before we do that, looking at the denominator, the square root. Let's go ahead and simplify that on the side. X squared minus seven. So X squared becomes seven. C can squared, and then we could pull out of seven. Factor it out. Then I could pull out the radical seven, and I can write C can't squared minus one as tangent squared, from which we have route seven times. Tan data. So this is our denominator. So coming back to the integral makes more room here. Okay, we have X and the numerator. So X's Route seven. So you can and then we have DX, which is route seven. Time's running out a room here. Let's come down here. C can't data tanta d data. So this is my numerator and then the denominator. We already simplify this. Yeah, Route 17 data. And then here we should cancel as much as we can. We see that we could cancel one of those roots, Evans. Also, the tension will go away and have this route seven up here. Let me go ahead and pull this out, okay? In front of the integral. And then we're left over with second time Second. So we have Seacon Square data detailer. Mhm. And this is one of the common in the rules that we've seen. We know the integral of this is just a tangent and at our constancy of immigration. So now at this point, we'll need to use a triangle because we want to express tanned data in terms of the original variable X. So we'll need a triangle here, So let's go to the next page. So we call our tricks up. X equals Route seven. Seek and data. Now, let's draw any right triangle that satisfies this property sloppy here. Okay, so let's go ahead and call this data over here. Now, If seeking of data is equal to X over route seven, let's go ahead and take the hype on Needs to be X and the adjacent side to be Route seven. Then if we choose these as our sides, then this equation appear is true. And then we could use Pythagorean theorem to find the remaining side each by Pythagorean theorem, we have this equation and then solving for age, we have radical X squared minus seven. Now going back to our original answer It was Route seven Tan Data plus E. Now we can go ahead and evaluate tangent potato. So we know tangent is opposite over adjacent. So we have route seven times H, Which is this over the adjacent room seven. Here. We see that we could cancel the Route seven's and we got our final answer Radical X squared minus seven plus c. And there'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
142
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell 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

01:10

Evaluate the integral. $\int \frac{x}{\sqrt{x^{2}-7}} d x$

03:02

Evaluate the integral. $$ \int 7^{x} \sqrt{1+7^{x}} d x $$

02:58

Evaluate the integral by substitution $$\int_{0}^{7} 2 x \sqrt[3]{x+1} d x$$

03:10

Use a substitution to evaluate the given integral. $$ \int\left(x^{2}+x\right) …

02:14

Evaluate the integral. $$\int_{1}^{7} \frac{2 x^{2}-3 x+5}{\sqrt{x}} d x$$

01:05

Evaluate the following integrals. $$\int \frac{d x}{\sqrt{x^{2}-49}}, x>7$$

01:17

Evaluate the definite integral. $ \displaystyle \int^1_0 \sqrt[3]{1 + 7x} \,…

02:04

Evaluate. $$\int_{0}^{\sqrt{7}} 7 x \sqrt[3]{1+x^{2}} d x$$

02:09

Evaluate the integral. $$ \int \frac{1}{\sqrt{7+6 x-x^{2}}} d x $$

01:02

Evaluate the definite integral. $\int_{0}^{1} \sqrt[3]{1+7 x} d x$

01:07

Evaluate the definite integral. $$\int_{0}^{1} \sqrt[3]{1+7 x} d x$$
Additional Mathematics Questions

01:50

(17) There is a narrow rectangular plot, reserved for a school. The length a…

02:18

The acceleration due to gravity on the moon is 1.6 m/s2. If an astronaut wei…

02:01

if (3x - 58)° and (x + 38)° are supplementary angles , find x and the angles…

01:42

Convert the following decimals into rational numbers(a) 1.16 if 6 have bar

00:57

Examine whether the solution set of the system of equations 3x - 4y = -7; 3x…

03:08

How many terms in the GP 4, 3.6, 3.24, ... are needed so that the sum exceed…

02:14

What is the final amount if 490 is increased by 15% followed by a further 14…

01:22

Find the perimeter of a square field of area 3969 sq. m

01:57

the ages of Rahul and Arun Aryan ratio 5 is to 7 four year later the sum of …

01:13

The ages of 10 men are: 32,51,38,64,45,36,33,43,48,50. What is the range of …

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