Search results

Re: MX2 2015 Integration Marathon Secret ways :p

Re: MX2 2015 Integration Marathon Sorry, it should be u = x+1 :)

Re: MX2 2015 Integration Marathon He used the substitution u = x+1 .

Re: MX2 2015 Integration Marathon FIXED

Re: MX2 2015 Integration Marathon (NEW) RECURRENCE QUESTION :) $ Let $I_n$ = $\int_{0}^{2\pi} (1+\cos\theta)^n \text{ d}\theta$, for $n > 0$. Show that $I_{n+1}=\frac{2n+1}{n+1}I_{n}$ $

Re: MX2 2015 Integration Marathon NEW QUESTION: $ Find $\int_{0}^{\frac{\pi}{4}} \frac{\text{ d}x}{\cos{x}\cdot{\sqrt\sec{x}-\tan{x}}}$ $

Re: MX2 2015 Integration Marathon NEW QUESTION :) $ Find $\int \tan(x)\cdot\tan(2x)\cdot\tan(3x) \text{ d}x$ $

It is like me asking you solve for x and y the following: 0(x) + 0(y) = 4.. No solution right? So the same applies above, you need to work with these constants to see if there exists parameters for your variables, and if they do exist, then you should get one parameter and express all your other...

@ mreditor16, this solution is probably the best one to follow and is most likely how they want you to deliver the proof without further knowledge. This question will never pop up in any of your class tests (or even final), since it is only trying to extend your understanding a little further...

Then you probably don't need to use matrices, since it is just a system of two equations in three unknowns, so you could solve it as if you are just solving a set of simultaneous equations and use the given conditions to work from there, since you already know the parametric/Cartesian form of a...

Once you get further through the course, you can then say the two distinct planes are parallel if and only if their normal vectors are parallel, otherwise they must intersect on a given line. Similiar to like in R^2, where if you have two distinct lines, they are parallel if and if only their...

I guess you could setup an augmented matrix [A|b] and get it to REF. Then examine at the last row and see what all the existing possibilities are for each entry. You will always find that one of the columns will be non-leading and hence one parameter will exist --> solution will be given by a...

Re: MX2 2015 Integration Marathon NEW QUESTION: $ Find $\int_{0}^{\infty} \frac{|x-1|}{(x+1)(x^2+1)} \text{ d}x$ $

Re: MX2 2015 Integration Marathon Your method? EDIT: Never mind, I saw that you substituted t = tan(x), which is a neat trick for this q :)

Re: MX2 2015 Integration Marathon EDIT. Apologies to all who attempted this, the upper limit is pi/4 not 1, too much posting of integration questions today has f*cked my brain up..

Re: MX2 2015 Integration Marathon For the indefinite case, if there is a substitution, it won't really work then you would need to be careful with the variables presented. The definite integral is always independent of the variable of integration, so it doesn't matter even if you use a...

Re: MX2 2015 Integration Marathon Oh, I see. Basically for any definite integral, it doesn't matter what our variable is, whether it is t or x or even u, since we have just assigned a name to it, so \int_{1}^{e} \ln{x} \text{ d}x = \int_{1}^{e} \ln{t} \text{ d}t = 1 (see how it doesn't matter...

Re: MX2 2015 Integration Marathon NEW QUESTION $ Find $\int_{0}^{\frac{\pi}{4}} \frac{\sec{x}}{\sqrt{\cos2x}} \text{ d}x$ $

Re: MX2 2015 Integration Marathon He just used the substitution u = -x to obtain the result. I think he skipped some of the steps due to cbf typing on LaTeX.

Re: MX2 2015 Integration Marathon NEW QUESTION: $ Find $\int_{-1}^{1} \tan^{-1}(e^x) \text{ d}x$ $