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

Order to solve mathematical operations, Order to solve Mathematical Operati...

Order to solve Mathematical Operations: Example: Solve the following equation: (4 - 2) + (3 x 4) - (10 ÷ 5) - 6 =  ____________ Solution: a.         Perform ma

Shoppers'' stop, How should shoppers''stop develop its demand forecasts?

How should shoppers''stop develop its demand forecasts?

Maths for Social Science, A retired couple has up to $30000 to invest in fi...

A retired couple has up to $30000 to invest in fixed-income securities. Their broker recommends investing in two bonds: one a AAA bond yielding 8%; the other a B+ bond paying 12%.

Multistage sampling, Multistage sampling Multistage sampling is similar...

Multistage sampling Multistage sampling is similar to stratified sampling except division is done on geographical/location basis, for illustration a country can be divided into

Product, a product can be anything including physical good,services,places,...

a product can be anything including physical good,services,places,experience,nations,organizations,properties,information.discuss the statement?

Solve the form ax2 - bx - c factoring polynomials, Solve the form ax 2 - b...

Solve the form ax 2 - bx - c factoring polynomials ? This tutorial will help you factor quadratics that look something like this: 2x 2 -3x - 14 (Leading coefficient is

Linear programming , use the simplex method to solve the following lp probl...

use the simplex method to solve the following lp problem. max z = 107x1 + x2 + 2x3 subject to 14x1 + x2 - 6x3 + 3x4 = 7 16x1 + x2 - 6x3 3x1 - x2 - x3 x1,x2,x3,x4 > = 0

Infinite interval - improper integrals, Infinite Interval  - Improper Inte...

Infinite Interval  - Improper Integrals In this type of integral one or both of the limits that is upper limit and lower limit of integration are infinity.  In these cases the

Explain expressions, Explain Expressions ? "One set of absolute value s...

Explain Expressions ? "One set of absolute value signs can only take the absolute value of one number." For example, For the absolute value of negative six plus three,

Which formula he use if he does not paint bottom of tank, Al is painting a ...

Al is painting a right cylinder storage tank. In sequence to purchase the correct amount of paint he requires to know the total surface area to be painted. Which formula will he us

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