Download the App!

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

Use the indicated entry in the Table of Integrals on the Reference Pages to evaluate the integral.

$ \displaystyle \int_1^2 \sqrt{4x^2 - 3}\ dx $ ; entry 39

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\sqrt{13}-\frac{3}{4} \ln (4+\sqrt{13})-\frac{1}{2}+\frac{3}{4} \ln 3$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 6

Integration Using Tables and Computer Algebra Systems

Integration Techniques

Missouri State University

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

01:53

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.

27:53

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

Use the indicated entry in…

06:04

Use the Table of Integrals…

05:18

03:55

03:45

04:03

$1-4$ Use the indicated en…

05:43

04:01

03:15

03:42

02:12

04:59

04:17

02:42

04:20

01:17

02:16

Okay, so this question wants us to use an integral table to find the value of this expression. So to do this, it wants us to use the following formula from the table. So in order to use this, we need to somehow transform this integral into the form you squared minus a squared. Well, in this case, it's pretty easy to see that a squared must be three. But what about are you? So we want to make you squared equal to four x squared, so you must be two times X. But now that we've introduced a u substitution, we have to remember to multiply by our general factor. Sophie, do do you? We find that it's two times DX so d X equals do you over too. So now we also need to transform our limits. So you of two is equal to well, two times two, which is four. And you of one is equal to two times one which is to So now, after all that work, we have the following expression. So our inter girl is equal to the integral from 2 to 4 of the square root of you squared minus three, which is route three squared, do you? With our factor of 1/2 from the change rule. So now this is in the exact form that our table in a girl isn't. So we can just substitute. So are integral is equal to 1/2 out front times You over too square root You squared minus three minus three over two times the natural log of you plus square root of you squared minus a squared And we're evaluating this whole thing starting at two and ending at four. So if we plug in upper limit minus lower limit, we see that we get square root of 13 minus 3/4 times the natural log. So four plus squared of 13 from our upper limit, minus 1/2 minus negative. 3/4 was a plus 3/4 Ellen of three. And there really isn't much we can do to simplify this. So this becomes our final answer

View More Answers From This Book

Find Another Textbook

01:10

Find the critical value F 0 to test the claim that 33 . Two sam…

03:28

QuestionLet X € {0, 1} and Y € {0, 1} be nvo independent …

02:03

Exercise 5 With the high cost of fuel and intense competition; the major air…

01:37

Clue is board game in which you must deduce three details surroundi…

02:11

QUESTION 20Tho owner 0 Cypres Recordinga Investlgated tha rolutionahip b…

03:27

In an experiment used to test the hardness reading associated with two tips …

04:15

Question 712.5 ptsAssume that we are interested in studying the inco…

03:41

facilities supervisor at sports Stadium wants to rate the condition…

02:23

50 people are randomty Relclod and the accuracy their wristwatches checked, …

02:29

QUESTION Electronic sensors certain type fail when they become too …