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

Simplified radical form, If we "break up" the root into the total of two pi...

If we "break up" the root into the total of two pieces clearly we get different answers. Simplified radical form: We will simplify radicals shortly so we have to next

Find out that sets of functions are linearly dependent, Find out if the fol...

Find out if the following sets of functions are linearly dependent or independent.  (a) f (  x ) = 9 cos ( 2 x )    g (  x ) = 2 cos2 (  x ) -  2 sin 2 (  x ) (b) f

digraph of r, Let R be the relation on S = {1, 3, 6, 9, 27} defined by aRb...

Let R be the relation on S = {1, 3, 6, 9, 27} defined by aRb iff a|b. (a) Write down the matrix of R. (b) Draw the digraph of R. (c) Explain whether R is reflexive, irrere

Example of learning constructing tables versus rote , Maya says thafl for i...

Maya says thafl for instance, to help the children of Class 2 construct the '5 times table', she uses their hands. Each child counts how many fingers on one hand, and then how ma

Find the value of the first instalment, A man arranges to pay a debt of Rs....

A man arranges to pay a debt of Rs.3600 in 40 monthly instalments which are in a AP. When 30 instalments are paid he dies leaving one third of the debt unpaid. Find the value of th

Quadratic equation, If roots of (x-p)(x-q) = c are a and b what will be th...

If roots of (x-p)(x-q) = c are a and b what will be the roots of (x-a)(x-b) = -c please explain. Solution)  (x-p)(x-q)=c x2-(p+q)x-c=0 hence,   a+b=p+q  and    a.b=pq-c

What is the difference in the two low temperatures, The low temperature in ...

The low temperature in Anchorage, Alaska present was -4°F. The low temperature in Los Angeles, California was 63°F. What is the difference in the two low temperatures? Visualiz

Concept, uses of maths concept

uses of maths concept

Which kevin gets paid is represented by x what does paid, Patrick gets paid...

Patrick gets paid three dollars less than four times what Kevin gets paid. If the number of dollars which Kevin gets paid is represented through x, what does Patrick get paid?

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