 ## Help! how to find intergral of absolute value of the sum of 2 odd functions?

for example

S(-1,1, |5^(1/2) * x^5 + 5*x^(1/5)|, X)

or intergrating |5^(1/2) * x^5 + 5*x^(1/5)| from x= -1 to 1

so i got the intergration of that whole function is

| sqrt(5)/6 + 25/6 * x^ (6/5) + c | from x= -1 to 1

when substituting the numbers in, it is:

squrt(5)/6 + 25/6 – ABS ( squrt(5)/6 + 25/6*(-1)^(6/5)

I’m stuck here. I can’t use the calculator because the question is „doing without the calculator„. Plus I want to be able to understand.

Since the function in side your abs value is odd, that means the function is (-) of what you get for + x values, if you consider -x values therefore you understand that the function integral for – values of x is the opposite sign of integral for + values of x

So just integrate it for +x from 0 to 1 and multiply the value by 2.

Or else you can consider the integral in two parts -1 to 0 first and 0-to 1 next. Pit -x instead of x for the integral from -1 to 0., there by you effectively get rid of ABs – sign.

E.g. Y= abs(x) means two functions

y = -x for x=0 it is same for functions like sin,
or odd powers.

Good luck!! ## what is the main use of c++ and java languages?

i am learning c++ these days. but i feel that the programs i am writing have no importance like the palindrome, odd even calculator etc. my tutor doesnt go beyond these sillly programs. i want to learn some real programs…..programs which have great potential and very good applications. can anyone help me??

You have to start somewhere and you need to understand basics first.

That said:

http://www.microsoft.com/express

Can get you up and making programs right now. ## Can someone help me! My graphing calculator broke!?

Using your graphing calculator graph the function f(x) = x4 – 4×3 + 3x + 5.

Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient. Explain why.

Degree is even because the highest exponent is even (its a 4).
The leading coefficient is positive, because x^4 is positive, and the graph goes up. ## Deterime whether the function is odd, even, or neither?

F(x) = x sin^3 x

I’m confused because I cant even input this into a calculator since I can’t put a sin^3 into it.
How do I find out what this is?

A function f(x) is even if f(x)=f(-x) and is odd if f(-x)=-f(x).
In this case:
f(-x) = – x* sin^3(-x) = x*sin^3 x
hence the function is even.

Edit: Another easy way is to see the graph:
An even function is perfectly symmetrical about y-axis, as you see in the link below. ## Could someone graph this function on an online graphing calculator for me?

I know it sounds stupid that I can’t do it myself on my own computer but I’m using an old computer that fails to install Java. I’ve tried looking for an online graphing calculator that doesn’t use Java and even free programs but haven’t come across any. Anyway, this is a simple way to help me out and get 10 points – basically just enter the function into a graphing calculator, take a screen capture of it, upload it onto an image hosting website and give a direct link to the picture.
The function is: f(x) = 2x-1/x+1 (I assume you can just literally copy and paste that into the graphing calculator).
I know it sounds like an odd and stupid question but I’ve struggled to sketch this graph and I just want to know whether I’ve sketched it correctly. I only want helpful answers, no unnecessary comments.
The „/“ is meant to indicate a fraction, not as to 1/x. Sorry. So, the function would be: 2x-1 / x+1 (2x-1 over x+1).

Http://goo.gl/lstxX is a PDF showing the answer in full.
Http://goo.gl/Fzgo8 is a link to the page with the solution. I don’t know if it’s using Java, but you can certainly give it a shot. It’s been very good at graphing, as well as showing different versions of the problem.