Example of integrals involving root - integration technique, Mathematics

Assignment Help:

Evaluate the following integral.

∫ (x+2 / 3√(x-3)) (dx)

Solution

Occasionally while faced with an integral that consists of a root we can make use of the following substitution to make simpler the integral into a form which can be easily worked with.

u = 3√(x - 3)

Thus, in place of letting u be the stuff under the radical as we frequently did in Calculus I we let u be the whole radical. Here, there will be a little more work here as we will as well need to know what x is thus we can substitute in for that in the numerator and thus we can compute the differential, dx. Though, this is easy enough to get.

Simply solve the substitution for x as follows,

 x = u3 + 3

dx = 3u2 du

By using this substitution the integral is now,

2165_Examples of Integrals Involving Root - Integration Technique.png


Related Discussions:- Example of integrals involving root - integration technique

Example of binomial distribution, Example:  Joanne is given a four-question...

Example:  Joanne is given a four-question multiple-choice quiz.  She hasnt studied the material to be quizzed, so she decides to answer the questions by randomly guessing the answe

Rounding whole numbers, Rounding whole numbers List the order in which ...

Rounding whole numbers List the order in which nancy, amy, ethel and cindy line up in single file to board the school bus. Then match the girls with their heights, which are fo

Trigonometric Identities, How to sovle or prove whether an equation is a id...

How to sovle or prove whether an equation is a identity?

Geometry, a figure is made of a rectangle and an isosceles right triangle. ...

a figure is made of a rectangle and an isosceles right triangle. the rectangle has sides of 6 in. and 3 in. one of the short sides of the rectangle is also one of the legs of the r

The sum of two consecutive integers is 41 integer, The sum of two consecuti...

The sum of two consecutive integers is 41. What are the integers? Two consecutive integers are numbers in sequence like 4 and 5 or -30 and -29, that are each 1 number apart. Le

Calculate how much ribbon is needed to wrap the box, Ribbon is wrapped arou...

Ribbon is wrapped around a rectangular box that is 10 by 8 by 4 in. Using the example provided, calculate how much ribbon is needed to wrap the box. consider the amount of ribbon d

Classification-developing pre-number concepts, Classification :  As you kn...

Classification :  As you know, classification (also called grouping) involves putting together things that have some characteristic in common. We can say that a child is able to c

Area problem, Area Problem Now It is time to start second kind of inte...

Area Problem Now It is time to start second kind of integral: Definite Integrals.  The area problem is to definite integrals what tangent & rate of change problems are to d

Solve cos( 4 ) = -1 trig function, Solve cos( 4 θ ) = -1 . Solution ...

Solve cos( 4 θ ) = -1 . Solution There actually isn't too much to do along with this problem.  However, it is different from all the others done to this point.  All the oth

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd