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

Find the root, (a) Convert z  = - 2 - 2 i to polar form. (b) Find ...

(a) Convert z  = - 2 - 2 i to polar form. (b) Find all the roots of the equation w 3 = - 2 - 2 i . Plot the solutions on an Argand diagram.

Level curves or contour curves - three dimensional space, Level Curves or C...

Level Curves or Contour Curves Another topic that we should look at is that of level curves or also known as contour curves. The level curves of the function z = f (x, y) are t

Illustration of simpson rule, By using n = 4 and all three rules to approxi...

By using n = 4 and all three rules to approximate the value of the following integral. Solution Very firstly, for reference purposes, Maple provides the following valu

Function and relation, how to know if it is function and if is relation

how to know if it is function and if is relation

Laplace transforms, In this section we will be searching how to utilize Lap...

In this section we will be searching how to utilize Laplace transforms to solve differential equations. There are various types of transforms out there into the world. Laplace tran

Evaluate the integral - trig substitutions, Example of Trig Substitutions ...

Example of Trig Substitutions Evaluate the subsequent integral. ∫ √((25x 2 - 4) / x) (dx) Solution In this type of case the substitution u = 25x 2 - 4 will not wo

Calculate the time average of kinetic energy of the planet, (1) If the coef...

(1) If the coefficient of friction between a box and the bed of a truck is m , What is the maximum acceleration with which the truck can climb a hill, making an angle q with the ho

Example of binomial distribution, Example:  Joanne is given a four-question...

Example:  Joanne is given a four-question multiple-choice quiz.  She hasnt studied the material to be quizzed, so she decides to answer the questions by randomly guessing the answe

Dimensional analysis, Rachel had 3.25 quart of ice tea. her family drank 9 ...

Rachel had 3.25 quart of ice tea. her family drank 9 cups.How many cups are left

History of Mathematics, What are the key features of Greek Mathematics? How...

What are the key features of Greek Mathematics? How does the emphasis on proof affect the development of Greek Mathematics?

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