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 quadratic equation using the quadratic formula, Find quadratic equatio...

Find quadratic equation using the Quadratic Formula: Solve the subsequent quadratic equation using the Quadratic Formula. 4x 2 + 2 = x 2 - 7x: Solution: Step 1.

Numbers, use the distributive law to write each multiplication in a differe...

use the distributive law to write each multiplication in a different way. the find the answer. 12x14 16x13 14x18 9x108 12x136 20x147

Properties of summation notation, Properties Now there are a couple of ...

Properties Now there are a couple of formulas for summation notation. 1. here c is any number. Therefore, we can factor constants out of a summation. 2. T

Pre Calculus, 5 2 ----- - ----- x-1 x+1 ------------------...

5 2 ----- - ----- x-1 x+1 -------------------- x 1 ----- + ----- x-1 x+1

Help, dividing decimals

dividing decimals

Share and dividend, to use newspaper and report on share and dividend

to use newspaper and report on share and dividend

Show that 571 is a prime number, Show that 571 is a prime number. Ans: ...

Show that 571 is a prime number. Ans:    Let x=571⇒√x=√571 Now 571 lies between the perfect squares of  (23)2 and (24)2 Prime numbers less than 24 are 2,3,5,7,11,13,17,1

Demonstrate that dijkstra algorithm - digraph, Demonstrate that Dijkstra's ...

Demonstrate that Dijkstra's algorithm does not necessarily work if some of the costs are negative by finding a digraph with negative costs (but no negative cost dicircuits) for whi

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