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Solve the given problems by integration.If an electric charge $Q$ is distributed along a straight wire of length$2 a,$ the electric potential $V$ at a point $P,$ which is at a distance $b$ from the center of the wire, is $V=k Q \int_{-a}^{a} \frac{d x}{\sqrt{b^{2}+x^{2}}} .$ Here, $k$ is a constant and $x$ is the distance along the wire. Evaluate the integral.

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 8

Integration by Trigonometric Substitution

Integrals

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

04:25

A thin rod carries charge …

01:20

The electric field in a re…

07:57

A charged rod of length $ …

09:50

(a) From the expression fo…

07:46

08:20

Evaluate the following int…

06:06

A rod of length $L$ lies a…

02:05

Use Gauss' Law for el…

06:01

To evaluate the fol. lowin…

04:05

A very long, solid cylinde…

in the problem we have been given the equal okay, q Integration of -8 to a dx upon whatever of B squared plus x square. To solve the problem we will assume x equal be done theater The X equals B six sq Tita de Tita. Well, first survey in different integral that is taxable. Sorry that is the ex upon road. Uvarov the square plus X square This is regional integration B six sq Tita de Tita upon. But under The Squire one plus dance party died. This is equal to be integration six Party to deter to upon B and here it is sector to this becomes integration shake theater Digital which is equal to Ellen mod Sector to plus 10 tita plus C. Now further this is written as Ellen mud X by B plus whatever off one plus X squared plus B squared. This is equal to Ellen model X five V plus right Uvarov, B squared plus X squared upon B and put the limit that is minus A to a. To put in the limit we have this equals two. Ellen mod A plus right Uvarov A square plus be a square upon minus eight plus. Cover off a squared plus B squared. So further we have finally, V equal que que el in mud A plus Todorov, A squared plus B squared upon minus a plus. Suvorov esquire plus B squared. So this is the final answer to the problem.

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