trig/logarithmic integral

[thesheepdog]

My textbook is very vague on dealing with integrals with trig and logarithms so hopefully someone on here can show me how it's done.

\(\displaystyle \int_0^{\sqrt{ln\pi}}2x e^x{^2} sin (e^x{^2}) dx\)]

A. \(\displaystyle -1\)

B.\(\displaystyle 1\)

C. \(\displaystyle 1- cos(1)\)

D. \(\displaystyle 1+cos(1)\)

 

[Deleted member 4993]

My textbook is very vague on dealing with integrals with trig and logarithms so hopefully someone on here can show me how it's done.

\(\displaystyle \int_0^{\sqrt{ln\pi}}2x e^x{^2} sin (e^x{^2}) dx\)]

A. \(\displaystyle -1\)

B.\(\displaystyle 1\)

C. \(\displaystyle 1- cos(1)\)

D. \(\displaystyle 1+cos(1)\)

Substitute:

\(\displaystyle \displaystyle{u \ = \ e^{x^{2}}}\)

du = ??

and continue...

 

[thesheepdog]

Substitute:

\(\displaystyle \displaystyle{u \ = \ e^{x^{2}}}\)

du = ??

and continue...

Can you show me an example of using "u" for substitution? I am trying to mentally picture what du looks like for this problem.

 

[stapel]

Can you show me an example of using "u" for substitution?

I'm sorry to hear that no examples were provided in your textbook or in your classroom lecture. Fortunately, there are loads of examples online. Please review at least two of the lessons at the link. Then, once you've learned the basic terms and techniques, please attempt the exercise, starting with the u-substitution provided by the other poster.

If you get stuck, you can then reply with a clear listing of your efforts so far, at which point we can begin to help you further. Thank you!

 

[HallsofIvy]

Can you show me an example of using "u" for substitution? I am trying to mentally picture what du looks like for this problem.

You say your text book is "vague on dealing with integrals". Are you also saying that you do not know how to differentiate? Do you know the "chain rule"?

 

[thesheepdog]

I know how to differentiate and I know what the chain rule is.

 

[notfromstatefarm]

Start with a U-substitution

You want to choose a U which will yield a dU that will cancel any remaining x-terms

As the previous poster stated, the best U here would be U= e^{x^2}

Which means dU= 2xe^{x^2}dx so dx=dU/(2xe^{x^2})

Now just substitute U and dU into the function and you will have a very simple integration (after simplifying). Also, don't forget to put the final answer back in terms of x.

 

[HallsofIvy]

I know how to differentiate and I know what the chain rule is.

Then why did you not answer Subhotosh Kahn's question in his first response- if \(\displaystyle u= e^{x^2}\) what is \(\displaystyle du\)?

 

[thesheepdog]

Y'all are some uptight people here.

 

[lookagain]

Y'all are some uptight people here.

Do not deflect onto us and attack the messengers.

You should have stated something along the lines of:

"You're right, HallsofIvy. I will try to do better on my part."

And then back that up with civil, meaningful posts.




Otherwise, please don't both bother posting to this help site.

 

[thesheepdog]

I will find help elsewhere.

 

[pka]

My textbook is very vague on dealing with integrals with trig and logarithms so hopefully someone on here can show me how it's done.

.
@thesheepdog, I am absolutely astonished that you or any other calculus student cannot just look at that problem and see the anti-derivative at once. The is nothing else to do except write it down.

What is the derivative of \(\displaystyle -\cos \left(e^{x^2} \right)~?\) So what is your answer to the OP?