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

Geometry homework, i just have one question i need help on for my geometry ...

i just have one question i need help on for my geometry homework

Methods for doing integral, There are really three various methods for doin...

There are really three various methods for doing such integral. Method 1: This method uses a trig formula as,  ∫sin(x) cos(x) dx = ½ ∫sin(2x) dx = -(1/4) cos(2x) + c

Method of reduction of order, Consider the equation x 2 y′′+ xy′- y = 4x...

Consider the equation x 2 y′′+ xy′- y = 4x ln x (a) Verify that x is a solution to the homogeneous equation. (b) Use the method of reduction of order to derive the second

Triganometry, Ask question #Minimum 100 words what is the hypotunus of a r...

Ask question #Minimum 100 words what is the hypotunus of a right bangled triangle a=5@ b=25 find c accwhepted#

Round 468.235 to the nearest hundredth, Round 468.235 to the nearest hundre...

Round 468.235 to the nearest hundredth ? The hundredths place is the second digit to the right of the decimal point (3). To decide how to round, you must like as at the digit t

Solve factors for given equations, 1/a+b+x  =1/a+1/b+1/x    a+b ≠ 0 ...

1/a+b+x  =1/a+1/b+1/x    a+b ≠ 0 Ans: 1/a+b+x  =1/a+1/b+1/x => 1/a+b+x -1/x = +1/a +1/b ⇒  x - ( a + b + x )/ x ( a + b + x )   = + a + b/ ab ⇒

Play and learn maths, PLAY AND LEARN :  Children can learn many basic math...

PLAY AND LEARN :  Children can learn many basic mathematical concepts through games. They enjoy Mathematical concepts can be playing within familiar contexts. Their games also gen

Formula to know the area of fan will wrap, Aaron is installing a ceiling fa...

Aaron is installing a ceiling fan in his bedroom. Once the fan is in motion, he requires to know the area the fan will wrap. What formula will he use? The area of a circle is π

Three person problem of points, Three-person Problem of Points: Pascal, Fer...

Three-person Problem of Points: Pascal, Fermat and their old friend the Chevalier de Mere each put $10.00 into a pot, and agree to play a game that has rounds. Each player has the

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