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

Hcf, the length of three pieces of ropes are 140cm,150cm and 200cm.what is ...

the length of three pieces of ropes are 140cm,150cm and 200cm.what is the greatest possible length to measure the given pieces of a rope?

#title.automotive cruise control system., What are some of the interestingm...

What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems

Fractions, how do you divide fractions?

how do you divide fractions?

Trignometry: sin-3x, sin(2x+x)=sin2x.cosx+cos2x.sinx              =2sinxco...

sin(2x+x)=sin2x.cosx+cos2x.sinx              =2sinxcosx.cosx+(-2sin^2x)sinx              =2sinxcos^2+sinx-2sin^3x             =sinx(2cos^2x+1)-2sin^3x =sinx(2-2sin^2x+1)-2sin^3

Communicating the meaning of addition, COMMUNICATING THE MEANING OF ADDITIO...

COMMUNICATING THE MEANING OF ADDITION :  One of the characters in a novel written by the Malayalam writer Vaikom Muhammed Basheer was asked by his teacher, "How much is one and on

what are the coordinates of the vertex , Use the graph of y = x2 - 6x  to ...

Use the graph of y = x2 - 6x  to answer the following: a)         Without solving the equation (or factoring), determine the solutions to the equation  x 2 - 6x = 0  usi

Parallel and perpendicular lines, The last topic that we have to discuss in...

The last topic that we have to discuss in this section is that of parallel & perpendicular lines. Following is a sketch of parallel and perpendicular lines. Suppose that th

Problem solver, a bathroom measure 250 cm by 175 cm calculate the side of t...

a bathroom measure 250 cm by 175 cm calculate the side of the largest square tile that can tile the floor

Probability rules, Probability Rules A probability is a number as...

Probability Rules A probability is a number assigned to the occurrence of an event in a sample space. Probability measures must satisfy three rules. If A is an even

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