Evaluate following. 0ln (1+)excos(1-ex)dx substitution, Mathematics

Assignment Help:

Evaluate following.

0ln (1 + π )  excos(1-ex)dx

Solution

The limits are little unusual in this case, however that will happen sometimes therefore don't get too excited about it.  Following is the substitution.

 u = 1 - ex                du = -ex dx

x =0               ⇒       u = 1 - e0  = 1 -1 = 0

x = ln (1 + π )  ⇒      u = 1 - eln (1+ π= 1 - (1 + π ) = - π

Then the integral is,

0ln (1 + π )  excos(1-ex)dx = ∫0(-∏) cosudu

                                  =-sin u|0(-∏)

                                  =  - sin (-∏)-sin0)=0


Related Discussions:- Evaluate following. 0ln (1+)excos(1-ex)dx substitution

Minimizing the sum of two distances, The value of y that minimizes the sum ...

The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.

What is the value of the lesser integer, The sum of three times a greater i...

The sum of three times a greater integer and 5 times a lesser integer is 9. Three less than the greater equivalent the lesser. What is the value of the lesser integer? Let x =

Fraction, 2 over 11 + 2 over 33

2 over 11 + 2 over 33

Ellipse, alpha and beta are concentric angles of two points A and B on the ...

alpha and beta are concentric angles of two points A and B on the ellipse.

Comparison test - sequences and series, Comparison Test Assume that we...

Comparison Test Assume that we have two types of series ∑a n and ∑b n with a n , b n ≥ 0 for all n and a n ≤ b n for all n.  Then, A.  If ∑b n is convergent then t

Unbounded intervals, Intervals which extend indefinitely in both the ...

Intervals which extend indefinitely in both the directions are known as unbounded intervals. These are written with the aid of symbols +∞  and -  ∞  . The various types

Calculate the profit of company, Company A and Company B have spent a lot o...

Company A and Company B have spent a lot of money on research to develop a cure for the common cold. Winter is approaching and there is certainly going to be a lot of demand for th

Generate pairs of vertices at random , Generate a 1000 vertex graph adding ...

Generate a 1000 vertex graph adding edges randomly one at a time.  How many edges are added before all isolated vertices disappear?  Try the experiment enough times to determine ho

Continuous compounding, If r per annum is the rate at which the princ...

If r per annum is the rate at which the principal A is compounded annually, then at the end of k years, the money due is          Q = A (1 + r) k Suppose

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