but the main problem here is whast the difference between an indefinite integral and a definite integral with dx? I know the integral sign from a to b dx means all the infinitely small pieces of x added together. But I don't understand the integral sign and dx together without area, like the above example. What does x stand for?
It is a basic theorem that, given a specific coordinate system, we can change a double integral into a repeated integral ("Fubini's Theorem"). Typically, we set up a problem in terms of a double integral and then change to a repeated integral to evaluate the integral.
Homework Statement Evaluate the line integral, where C is the given curve. integral of xy^4. C is the right half of the circle x^2 + y^2 =16 Homework Equations integral of line integral= integral of r(t) |r'(t)| dtThe Attempt at a Solution I set up a parametric equation to be r(t)=(4cost...
So, since you cannot integrate sin (x 2) in elementary functions, reverse the order of integration, as I suggested.
0 May 15, 2006 #4 yes ment L^2 not y^2 at the bottom.. thanks for pointing out that. so nobdy who knows exatcly how one goes from the firs tpoint of the bio savart law to the later (stated in the first post) yeah so let's sat that we can use the trig but then how do i get it out to "normal" form so i can evaluate?
1 Dec 16, 2005 #5 integral(x^2-1)^(1/2)dx just rewrite it like that and I think you will se how to solve it. Remember to divide with the inner derivate of the function. Unless I am missing something in the formulation of the question no variable substitution is needed. Cite Cite this post
Do anyone have an idea how to calculate integral of (cos x)^2 ? Or is it even possible? I tried some substitutions and/or rules of trigonometry, like...
While the derivative of ln(x) is 1/x, its integral certainly is not. you can find its integral by parts (product rule). If you want the derivative of ln(f(x)) for some function f, use the chain rule.
Well, so I really want to integrate what's shown in the title: i.e. \\int \\frac{dx}{(x^2+y^2)^\\frac{3}{2}} Now, I know there are quite a few straightforward answers to this. But what I really want is how people who do math got this formula in the first place. I don't just want a formula that...