Ephilo
find the integral.



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rosjua
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5^x/(log(5))+C

Ephilo
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dw:1361280612277:dw

mathsmind
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i have been trying to enter the site since yesterday did you all have the same problem?

mathsmind
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anyways there are many ways to solve this problem, one of them would be Taylor series the other one would be substitution method

Ephilo
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@mathsmind yea ive been having problems with it to so i did the problems i know how to do until it finally works

Ephilo
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@mathsmind i figured that one out im stuck on another one now

Ephilo
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evaluate the intergal dw:1361284859202:dw

Ephilo
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@mathsmind that one ^^^

mathsmind
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sorry i meant i was having problems entering the website since yesterday

mathsmind
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i know how to solve both integral in my head

Ephilo
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@mathsmind how long are you going to be one today ?

mathsmind
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it depends on my work, if i am busy or not

mathsmind
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can you answer my question please?

mathsmind
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were you able to log on to the site

Ephilo
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@mathsmind which one ? lol

Ephilo
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oh no i wasnt i answered it above

mathsmind
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this website? openstudy

Ephilo
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it wasnt loading

Ephilo
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i felt like crying lol, with out this website i don't know what id do

mathsmind
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ok let me reply to the last integral

mathsmind
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the answer for the last integral would be pi/6

mathsmind
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now by looking at the last integral you can find out from the table that it is equal to arcsin(x/2)

Ephilo
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for the 4x?

mathsmind
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\[\int\limits_{0}^{1}\frac{ dx }{ \sqrt{4x^2} }\]

mathsmind
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is that the integral or not?

Ephilo
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yepp

mathsmind
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the answer is pi/6

Ephilo
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how did you get it?

mathsmind
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ok there are two ways to do that

mathsmind
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one way is to look at the arctrigs integrals

mathsmind
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you know the table of integrals right!

mathsmind
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the other way is to go through full substitution method

Ephilo
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lol no but ill look them up

mathsmind
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ok do you want detailed solution then

Ephilo
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the u sub thing ?

mathsmind
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yep

mathsmind
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you let x=2u

mathsmind
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x^2 = 4u^2

Ephilo
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okay i get it so far

mathsmind
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can you differentiate the last bit?

mathsmind
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dx = 2du

mathsmind
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\[\int\limits_{0}^{1}\frac{ 2du }{\sqrt{44u^2} }\]

mathsmind
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\[\int\limits\limits_{0}^{1}\frac{ du }{\sqrt{1u^2} }\]

Ephilo
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your a math genuis lol

mathsmind
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thanks that was kind of you, and you are a bright student

mathsmind
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let me give you a third way how to do that

Ephilo
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i understand the usub the most

Ephilo
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i have three more integral questions

mathsmind
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ok go ahed

mathsmind
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you need to know different methods to solve one problem , that for future note...

Ephilo
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altho the differentiate part is a bit hard

mathsmind
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i have a phone call but still submit your work

Ephilo
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but ill look back it later because i have to get this course done to graduate

mathsmind
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no i meant you make y =2sinx sub

mathsmind
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different substitution

mathsmind
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if you look at the unit triangle you can figure out that you need a sin sub

Ephilo
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okay

Ephilo
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find the intergal dw:1361286908472:dw

mathsmind
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again you are going to get an arctan but now we need to look at the factors

mathsmind
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just by looking at this integral we will get 4/3arctan(3x) +c

mathsmind
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the question is what was x=? in this u sub

mathsmind
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you need to assume that 3x=u, 9x^2=u^2, 3dx=du

mathsmind
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\[\int\limits \frac{ 4du }{ 3(1+u^2) }=\frac{ 4 }{ 3}\arctan(u)+c\]

mathsmind
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\[u=3x, \therefore \frac{ 4 }{ 3 }\arctan(3x)+c\]

mathsmind
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that's your final answer

Ephilo
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okay i just did the other one so i have one more integral question

Ephilo
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dw:1361287534741:dw

mathsmind
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ok

mathsmind
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again you can see we will get the arctan + something

mathsmind
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your answer should be\[\frac{ 1 }{ 2 }\arctan(\frac{ 1 }{ 2}(x1))+c\]

mathsmind
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\[\int\limits\limits\limits \frac{ dx }{4+(1x)^2}\]

mathsmind
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now 2u=1x, 4u^2=(1x)^2,

mathsmind
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now one thing you need to know is how to let the 4 be a one in the denominator

Ephilo
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how do i know that?

mathsmind
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ok let me show, it is clear from the usub

mathsmind
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remember that 2u =1x, 2du=dx

Ephilo
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okay so far so good lol

mathsmind
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\[\int\limits\frac{ 2du }{4(1+(u)^2)}\]

mathsmind
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can you see it better this way?

mathsmind
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\[\frac{ 1 }{ 2 }\arctan(u)+c\]

mathsmind
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\[2u=1x, \space u=\frac{ 1 }{ 2 }(1x)\]

mathsmind
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\[\frac{ 1 }{ 2 }\arctan(\frac{ 1 }{ 2 }(1x))+c\]

mathsmind
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that's your final answer

Ephilo
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okay thanks ! im working on some ill let you know if i need more help

mathsmind
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you don't sound like you got the last one?

Ephilo
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lol i havent fully looked at it yet im finishing a problem

mathsmind
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ok

mathsmind
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so i read your mind well hehehe

Ephilo
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lol yeahh i was wondering how you knew that,but im looking at it now

mathsmind
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i still don't understand how the engagement scheme works on open study

Ephilo
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i get that one

mathsmind
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good

Ephilo
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i think its by the questions you answer, and medals you receive

mathsmind
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no i am not asking about those two, i am asking about the engagement part

mathsmind
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the one that has learner next to it

Ephilo
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lol i thinks its from asking questions cause thats how you learn right

Ephilo
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okay i found two i need help on

mathsmind
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go ahead

Ephilo
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determine which of the integrals can be
found using the basic integration formulas you have studied
so far in the text.

mathsmind
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i think you need to open a new thread because this one is getting heavy with BW

Ephilo
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lol okay i will