Recent content by nayfie

Thank you both for the replies, very helpful!

Homework Statement -- Homework Equations -- The Attempt at a Solution This isn't really a proper homework question so I'll just write my problem here: I'm trying to compute a closed line integral over a triangular region. I have calculated two of the sides, but am now left...

Firstly, thanks for the reply. Can you describe what you mean by a parametrization? In your example you've used a range, but in an example we did in class the lecturer used the function of the curve. I'm confused :(

Hey guys. I've just had a few lectures on line integrals. My lecturer has told me the following: \int_{C}^{} f(s) \text{d}s = \int_{a}^{b} f(\gamma(t))\|\gamma'(t)\| \text{d}t Unfortunately he hasn't explained this topic very well. I understand what's going on with a line integral but have...

Took your advice and the answer popped out straight away. How did I not think of this? Thanks mate :)

I haven't been taught that yet. Is that the only way to solve this integral? I've been reading the related articles but can't work out how to apply it to this question. Unfortunately it seems my physics course is ahead of my maths course.

Homework Statement I'm having difficulty solving the following integral. \int_{-\infty}^{\infty} x^{4}e^{-2\alpha x^{2}} \text{d}x Homework Equations \int_{-\infty}^{\infty} e^{-\alpha x^{2}} \text{d}x = \sqrt{\frac{\pi}{\alpha}} \int_{-\infty}^{\infty} x^{2}e^{-\alpha x^{2}}...

Just took another look at this question and might have solved it. u = (a, b), v = (c, d), u + v = (a + c, b + d) (a + c)^{2} + (b + d)^{2} = 0 a^{2} + 2ac + c^{2} + b^{2} + 2bd + d^{2} = 0 But, we know from the constraints of the subspace that; a^{2} + b^{2} = 0; c^{2} + b^{2} = 0...

Hello :) I've been doing a lot of work on subspaces but have come across this question and need a bit of help! Homework Statement W = {(x, y) \in R^{2} | x^{2} + y^{2} = 0} Homework Equations 1. 0 ∈ W 2. ∀ u,v ∈ W; u+v ∈ W 3. ∀ c ∈ R and u ∈ W; cu ∈ W The Attempt at a...

:) Thank you all very much for the help!

Actually now that I look at it again I think the chain rule needs to be applied twice? f(x) = G(cosh(x^{2})) f'(x) = G'(cosh(x^{2})) = g(cosh(x^{2})).sinh(x^2).2x f'(x) = tanh(cosh^{2}(x^{2})).sinh(x^{2}).2x It's been a long day :(

First of all, thank you all for the contributions :) I think I have arrived at an answer! Let me know if I've made a mistake. ----------------------------------------------------------------- f(x) = \int^{cosh(x^{2})}_{0} tanh(t^{2})dt, let tanh(t^2) = g(t) f(x) = G(cosh(x^{2})) -...

You mean that \frac{d}{dx} \int^{x}_{a} f(t)dt = f(x)? Does this imply that \frac{d}{dx} \int^{cosh(x^{2})}_{0} tanh(t^2)dt = tanh(cosh^2(x^2))?

Hello again :) I get the feeling I'm missing some kind of 'trick', as this is proving a very difficult question :( I'll write out my frustration below; Homework Statement Find f'(x) if f(x) = \int^{cosh(x^{2})}_{0} tanh(t^2)dt Homework Equations --- The Attempt at a Solution My idea was...

I have followed both of your replies and have proven that W is indeed a subspace (as it satisfies the conditions). I find it easier to understand what's going on if I have a geometric interpretation. Thank you both very much for the replies, you've ended a lot of frustration :)