Additionally functions in substitution rule, Mathematics

Assignment Help:

Substitution Rule

Mostly integrals are fairly simple and most of the substitutions are quite simple. The problems arise in correctly getting the integral set up for the substitution(s) to be done.  Once you illustrate how these are done it's simple to see what you ought to do, however the first time through these can cause problems if you aren't on the lookout for potential problems.

Example Evaluate following integrals.

      ∫ e2t  + sec ( 2t ) tan ( 2t ) dt

Solution

This integral contains two terms in it and both will need the similar substitution. This means that we ought not to do anything special to the integral. One of the more common "mistakes" here is to break the integral and carry out a separate substitution on each of the part. It isn't really mistake although will definitely enhance the amount of work we'll have to do.  Therefore, since both terms in the integral utilizes the similar substitution we'll just do everything like a single integral by using the following substitution.

                     u = 2t                          du = 2dt⇒           dt = 1/2 du

Then the integral is,

∫ e2t  + sec ( 2t ) tan ( 2t) dt = 1/2 ∫ eu  + sec (u ) tan (u ) du

= 1 /2(eu  + sec (u ))+ c

= 1/2 (e2t  + sec ( 2t )) + c

Frequently a substitution can be utilized multiple times in an integral thus don't get excited about that if it happens.  Also note as well that since there was a  ½ in front of the whole integral there have to be a  1 /2 also in front of the answer from the integral.


Related Discussions:- Additionally functions in substitution rule

Coordinate geometry, find the value of x for which the distance between the...

find the value of x for which the distance between the points p(4,-5) and q(12,x) is 10 units

Angles, samuel left mauritius at 22:30 on saturday and travelled to london ...

samuel left mauritius at 22:30 on saturday and travelled to london (GMT) for 14h30min he had a stopover for 4 h in london and he continued to travel to toronto for another 6h20min

Probability, There are 20 defective bulbs in a box of 100 bulbs.if 10bulbs ...

There are 20 defective bulbs in a box of 100 bulbs.if 10bulbs are choosen at random then what is the probability of there are just 3defective bulbs

Number system, NATURAL NUMBERS The numbers 1, 2, 3, 4.... Are called as...

NATURAL NUMBERS The numbers 1, 2, 3, 4.... Are called as natural numbers, their set is shown by N. Hence N = {1, 2, 3, 4, 5....} WHOLE NUMBERS The numbers 0, 1, 2, 3, 4

Vectors, |a.x|=1 where x = i-2j+2k then calculate a

|a.x|=1 where x = i-2j+2k then calculate a

Substitute 6 for r in the formula a = r^2 and solve for a, Find the area of...

Find the area of a circle along with a radius of 6 inches. The formula for the area of a circle is A = πr 2 . Use 3.14 for π. Substitute  6 for r in the formula A = πr 2 and solve

Estimates the probabilities of price changes, Mr. Hoper is in charge of inv...

Mr. Hoper is in charge of investments for the golden horizon company. He estimates from past price fluctuations in the gold market that the probabilities of price changes on a give

Geometry, Ask question A triangle has two sides that measure 23 ft and 30 f...

Ask question A triangle has two sides that measure 23 ft and 30 ft. Which could be the measure of the third side? A. 5 ft B. 7 ft C. 10 ft D. 53 ft #Minimum 100 words accepted

The shape of a graph, The Shape of a Graph, Part II : In previous we saw h...

The Shape of a Graph, Part II : In previous we saw how we could use the first derivative of a function to obtain some information regarding the graph of a function.  In this secti

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