Please Help me With Calculus: Integrals! and Derivative Prob

[nuvydeep]

Hello to my lovely fellow math help forum posters,

I am in need of help with the following problems involving evaluating integrals. I took a picture of the problems that I need help with. It's 3 integral problems and 1 derivative problem involving max/min etc.

I would appreciate any help that can be given!!! I need help on the steps to this method.. step by step. Can someone write the steps out and take a picture of it and post it up because its easier than writing *int* instead of the integral sign? :?:

Thanks

 

[galactus]

Spelling \(\displaystyle {\pi}\) as PIE is a bad sign. This calls for ribbin' before I continue.

This is math, not a pastry class.


\(\displaystyle \int_{0}^{\pi}sin(x)cos^{2}(x)dx\)

Let \(\displaystyle u=cos(x), \;\ -du=sin(x)dx\)

Make the sub and it turns into an easy integration.

\(\displaystyle \int\frac{1}{x}cos(ln(x)+1)dx\)

Let \(\displaystyle u=ln(x)+1, \;\ du=\frac{1}{x}dx\)

\(\displaystyle \int x^{2}e^{-x}dx\)

Try using parts.

Let \(\displaystyle u=x^{2}, \;\ dv=e^{-x}dx, \;\ du=2xdx, \;\ v=-e^{-x}\)

Parts will have to be applied again, then it falls into place.

There are other ways to go about it, but this is about as good as any.

 

[Deleted member 4993]

Hello to my lovely fellow math help forum posters,

I am in need of help with the following problems involving evaluating integrals. I took a picture of the problems that I need help with. It's 3 integral problems and 1 derivative problem involving max/min etc.

I would appreciate any help that can be given!!! I need help on the steps to this method.. step by step. Can someone write the steps out and take a picture of it and post it up because its easier than writing *int* instead of the integral sign? :?:

Thanks

These look like problems from a take-home test.

Are you going to declare on the front page of your answer book that you asked for and received "step-by-step" assistance from internet?

 

[galactus]

What I done is hardly step-by-step. I just supplied the sub for the first two. It is up to the poster to finish.

The third one will have to have parts applied a second time.

 

[Deleted member 4993]

What I done is hardly step-by-step. I just supplied the sub for the first two. It is up to the poster to finish.

The third one will have to have parts applied a second time.

Cody,

I am sorry - I did not mean that your answer was step-by-step. Somehow when I wrote my response - your response was not visible to me (I think I started to write it - got distracted - came back sometime later and posted it). However, as you know, there will be step-by-step full response coming - I was referring to the inevitable future!!!

As a matter of fact - I agree with your way of responding. I only wish I did not have the sneaky suspicion that the problem-set is from a take-home test (or test from an on-line class). S/he also posted at:

http://www.mathhelpforum.com/math-help/ ... w-pic.html

Khan

 

[pitoten]

Hey, where were those take home tests when I was in my math classes? :roll:

 

[nuvydeep]

This is extra credit Each point received counts as 1/4th of a test point on the final. Final is comprehensive :/

 

[BigGlenntheHeavy]

\(\displaystyle 7) \ f(x) \ = \ x^3-3x+3\)

\(\displaystyle f'(x) \ = \ 3x^2-3 \ = \ 0, \ \implies \ x \ = \ \pm1\)

\(\displaystyle f"(x) \ = \ 6x \ = \ 0, \ \implies \ x \ = \ 0\)

\(\displaystyle f(1) \ = \ 1, \ rel. \ min., \ 2nd \ derivative \ test.\)

\(\displaystyle f(-1) \ = \ 5, \ rel. \ max., \ 2nd \ derivative \ test.\)

\(\displaystyle f(0) \ = \ 3, \ point \ of \ inflection, \ see \ graph \ below, \ you \ should \ be \ able \ now\)

\(\displaystyle to \ take \ care \ of \ any \ particulars.\)

[attachment=0:2ua5qv0d]hhh.jpg[/attachment:2ua5qv0d]

 

[nuvydeep]

\(\displaystyle f(x) \ = \ x^3-3x+3\)

\(\displaystyle f'(x) \ = \ 3x^2-3 \ = \ 0, \ \implies \ x \ = \ \pm1\)

\(\displaystyle f"(x) \ = \ 6x \ = \ 0, \ \implies \ x \ = \ 0\)

\(\displaystyle f(1) \ = \ 1, \ rel. \ min., \ 2nd \ derivative \ test.\)

\(\displaystyle f(-1) \ = \ 5, \ rel. \ max., \ 2nd \ derivative \ test.\)

\(\displaystyle f(0) \ = \ 3, \ point \ of \ inflection, \ see \ graph \ below, \ you \ should \ be \ able \ now\)

\(\displaystyle to \ take \ care \ of \ any \ particulars.\)

[attachment=0:2p4mhtfb]hhh.jpg[/attachment:2p4mhtfb]

Thank you for the post, I agree with you about everything except for the maxima and minima. Shouldn't the maxima be (-1,5) and the minima be (1,1) ? Correct me if I am wrong..

 

[BigGlenntheHeavy]

That is what I have. ?????????