Edit: Nevermind, that's derivatives. Hold on.
Hi,
I am having trouble evaluating the indefinite integral of the following problem using U-substitution. The answer at the back of the book is 2sin square root of t + C. I'm not sure what U should be. Any assistance will be appreciated. Thanks in advance.
1. The problem statement, all variables and given/known data
Evaluate the indefinite integral
2. Relevant equations
integral of cos * (square root of t) / (square root of t) dt
3. The attempt at a solution
integral of cos * (square root of t) / (square root of t) dt
Let U = ?
Lets say U = cos * (square root of t)
du = sin * (square root of t) dx
This does not make any sense to me. Im I going right? Where did I go wrong?
Thanks for taking the time to help me with this Deadstar. I really appreciate this.
Wow, what you posted was an eyefull, unfortunately, I don't understand. Ok, I am new to this, but from my understanding (correct me if I am wrong), I am supposed to use U-substitution, meaning I am supposed to assign U = something, then find du = the derivative of something dx, etc etc. Can you tell me what should I assign U = to?
Do you have to solve it that way or is that what you think you have to do. I did not use a u-substitution method.
The way I solved it was to expand as a power series.
See part 3 here. Trigonometric functions - Wikipedia, the free encyclopedia
Then divided it through by to get the integral in your question.
Then I used the fact...
The integral of a sum is the sum of an intergal.
This basically just follows from the following property of integrals.
So all I had to do was integrate the sum formula that generated my series which was...
Which is equal to the power series for multiplied by .
I.e. I did this...
=
=
(why?)
because...
=
=
=
=
=
=
Then I just realized it was almost the same as the power series for but multiplied by 2.
Have a look at that link and you'll see the series expansions for cos and sin. Just put where the x's are and you get my series.
wow!!!!!!!! its nice but sparky your right with your idea...he just explore it to understand be easily...keep doin that i like calculus so much actually all kinds of math...
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