Example of integration by parts - integration techniques, Mathematics

Assignment Help:

Example of Integration by Parts - Integration techniques

Illustration1:  Evaluate the following integral.

∫ xe6x dx

Solution :

Thus, on some level, the difficulty here is the x that is in front of the exponential.  If that was not there we could do the integral.  Notice also, that in doing integration by parts anything that we wish for u will be differentiated.  Thus, it seems that choosing u = x will be a good choice as upon differentiating the x will drop out.

Here that we've selected u we know that dv will be everything else which remains.  Thus, here are the choices for u and dv also du and v.

u = x    dv = e6x dx

du = dx           v = e6x dx = 1/6e6x

Then the integral is as follow:

∫ xe6x dx = x/6 e6x - ∫ 1/6 e6x dx

= x/6 e6x - 1/36 e6x + c

Just once we have completed the last integral in the problem we will add in the constant of integration to obtain our final answer.


Related Discussions:- Example of integration by parts - integration techniques

Regrouping, in regrouping if we have abig number in the end what should i d...

in regrouping if we have abig number in the end what should i do?add an number on top of it,please help

How do you traverse a binary tree, How do you traverse a Binary Tree?  Desc...

How do you traverse a Binary Tree?  Describe Preorder, Inorder and Postorder traversals with example.     Ans: Traversal of tree means tree searching for a aim. The aim may be

Functions, find the domain of the function f(x) = (| sin inverse sin x | - ...

find the domain of the function f(x) = (| sin inverse sin x | - cos inverse cos x) ^ 1/2

Diffrential integral , All the integrals below are understood in the sense ...

All the integrals below are understood in the sense of the Lebesgue. (1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]

Find the third vertex of a triangle, Find the third vertex of a triangle if...

Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid point of one side is (0, 3).

Law of Iterative Expectation, #quesSuppose we have a stick of length L. We ...

#quesSuppose we have a stick of length L. We break it once at some point X ~ Unif(0;L). Then we break it again at some point Y ~ Unif(0;X). Use the law of iterated expectation to c

Word problem, mark got 15.00 for his birthday he now has 27.00. how much di...

mark got 15.00 for his birthday he now has 27.00. how much did he start with

Graph and algebraic methods , To answer each question, use the function t(r...

To answer each question, use the function t(r) = d , where t is the time in hours, d is the distance in miles, and r is the rate in miles per hour. a. Sydney drives 10 mi at a c

Least common denominator using primes, Least Common Denominator Using Prime...

Least Common Denominator Using Primes: A prime number is a whole number (integer) whose only factors are itself and one. So the first prime numbers are given as follows: 1,

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