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

Scatter graphs, Scatter Graphs - A scatter graph is a graph that compr...

Scatter Graphs - A scatter graph is a graph that comprises of points which have been plotted but are not joined through line segments - The pattern of the points will defin

Examples on probability, 1. A machine comprises of three transformers A, B ...

1. A machine comprises of three transformers A, B and C. Such machine may operate if at least 2 transformers are working. The probability of each transformer working is given as di

Interpretations of the derivative , Interpretations of the Derivative : ...

Interpretations of the Derivative : Before moving on to the section where we study how to calculate derivatives by ignoring the limits we were evaluating in the earlier secti

Differences of squares and other even powers, Differences of Squares (and o...

Differences of Squares (and other even powers) ? A square monomial is a monomial which is the square of another monomial. Here are some examples: 25 is the square of 5 x 2 i

Hours, jeff left hartford at 2:15 pm and arrived in boston at 4:45 pm how l...

jeff left hartford at 2:15 pm and arrived in boston at 4:45 pm how long did the drive take him?

Modeling with first order differential equations, We here move to one of th...

We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a

Math, weather prediction on monsoon past data on project

weather prediction on monsoon past data on project

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