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

Calculus (The squeeze theorem), When finding the limit as x approaches 0 th...

When finding the limit as x approaches 0 the for function (square root of x^3 + x^2) cos(pi/2x) would the limit not exist because there would be a zero in the denominator?

Multiplication and division, you want to share 34 pencils among 6 friends ....

you want to share 34 pencils among 6 friends .How many would each friend get?

Smith keeps track of poor work, Smith keeps track of poor work. Often on af...

Smith keeps track of poor work. Often on afternoon it is 5%. If he checks 300 of 7500 instruments what is probability he will find less than 20 substandard?

4th grade, Ray cut 6 pieces of rope . Each piece was between 67 and 84 inch...

Ray cut 6 pieces of rope . Each piece was between 67 and 84 inches long. What would be the total length of the 6 pieces of rope?

Basic set union operation, Q. Basic Set Union Operation? Ans. Supp...

Q. Basic Set Union Operation? Ans. Suppose instead that your school needs to know which students are taking either art or business or both. Then the students who are ta

prove that 2a=b+c, If the roots of the equation (a-b) x 2 + (b-c) x+ (...

If the roots of the equation (a-b) x 2 + (b-c) x+ (c - a)= 0 are equal. Prove that 2a=b+c. Ans:    (a-b) x 2 + (b-c) x+ (c - a) = 0 T.P 2a = b + c B 2 - 4AC = 0

staticis, a statisics professor plans classes so carefully that the length...

a statisics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. find the probability that a given class pe

Mensuration of plane figures, a sail has a spread of canvas as measured 12'...

a sail has a spread of canvas as measured 12'',12'', 15'' and 9'' and it has 90 degrees. Find the area of one side of the sail

Cluster sampling, Cluster Sampling Cluster sampling is where a few geog...

Cluster Sampling Cluster sampling is where a few geographical regions for illustration, a location, village or town are selected at random and say every single household or sho

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