Wow, you're quick! Thanks for the help, Dick. I was hoping there would be a less tedious method to go about solving problems such as these, but I guess that's math for ya'.
Thanks again!
Homework Statement
$$\int_{0}^{\ 2\pi} \ |e^{sin(x)}cos(x)| \, dx$$
I know that it simplifies to $$ 2e- \frac{2}{e} ≈ 4.7 $$ I'm not sure how to approach this problem. Do I just break the integral up into the domains where it's positive and negative and integrate each component...
Hey Dick,
Thanks for your reply. I suppose we haven't learned trig substitution yet, so I guess that's my problem.
As for the dx, doesn't that mean 'in respect to x'?
Thanks!
Homework Statement
Evaluate
$$\int_ \ \sqrt[2]{9-x^{2}} \, \mathrm{d} x.$$
Homework Equations
U substitution
Integration by parts
The Attempt at a Solution
My teacher said it wasn't possible "by hand", but Wolframalpha provided a step-by-step solution. I'm clueless as to how wolfram came...
Homework Statement
Find the local extrema of the function f(x)=(x^3-2x-2cos(x))
Homework Equations
derivatives, some algebra
The Attempt at a Solution
Well, the concept is simple.
Solve for the first derivative and set it equal to zero:
dy/dx=2sin(x)+3x^2-2=0 and
Next, solve for x to...
I'm sorry, but I haven't learned this yet, but I think you guys are saying that Wolfram should have labeled it an "alternate form assuming x is real" (rather than just positive).
Excuse my ignorance, but what's the difference and how does this relate to Wolfram's statement that x has to be...
Well, it turns out that $$-\frac{4}{x\sqrt{x^8-1}}≠-\frac{4}{x^5 \sqrt{1-\frac{1}{x^8}}}$$ at least according to Wolfram.
http://www.wolframalpha.com/input/?i=-4%2F%28x*sqrt%28x%5E8-1%29%29%3D-4%2F%5Bsqrt%281-%281%2F8%29%29*%28x%5E5%29%5D...
Perhaps Alternate form assuming x is positive doesn't mean that the input x has to be positive. Maybe it's referring to the function as a whole (or something else)?
Wolfram says the samething when I input:
##\sqrt{x^8}##
and that ##x^8## is an alternate form assuming x is positive, but...
Could you please elaborate on this?
Please correct me if I'm wrong, but I think that statement would be correct only if it were ##\pm\sqrt{x^8}##, but it's only ##\ +\sqrt{x^8}##
Plus, how did you isolate ##\sqrt{x^8}## from ##\sqrt{x^8-1}##?
Hello Simon,
Thanks for your reply. The form Wolfram gave me was:
-4/[sqrt(1-(1/8))*(x^5)]
http://www.wolframalpha.com/input/?i=dy%2Fdx+of+arcsin%281%2Fx%5E4%29
I still don't see where the 'simplified form' that I derived and this form differ.
Homework Statement
Find dy/dx of arcsin(1/x^4)
2. The solution
Answer simplified:
-4/(x*sqrt(x^8-1))
I've checked my answer to the above problem on WolframAlpha, and Wolfram states that the answer is "an alternate form assuming x is positive"
I guess this is more of a...
This is more a conceptual question, but after watching several videos about Quantum Mechanics, I noticed a little discrepancy about an explanation of the double slit experiment and it's implications.
According to one video, the electron fired traveled through both slits at the "same time as...
Today, my teacher showed us a video in class (AP physics B) as part of our quantum physics unit.
I'm really skeptical about the video, and I wanted to seek the opinion of people who are actually knowledgable in this field. Is there anything wrong with the information provided...
It's been a few days since first seeing this problem.
I asked another math teacher, and he literally spent an entire class trying to solve it. My teacher has asked other teachers, and they haven't figured it out yet.
I've worked the left side down to...
Homework Statement
(tan/(1-cot))+(cot/(1-tan))=1+(sec)(csc)
The Attempt at a Solution
This problem showed up in my class as a warm-up, and when my teacher tried to solve it for us he got stuck. I've asked a few classmates in higher level math, and they all seem to get stuck.
I...
It seems like everyone I know believes that probability is much easier than Calc, but I believe that's a subjective point of view.
I know that Calculus has various levels (i.e. I,II,III), but is it really all that much more difficult than probability?
How many different 'levels' of probability...
Alright, I think I can visuallize it now.
Basically, I take 180-(first angle) and I should get my second angle.
Thanks!
P.S. Do I do the same thing for the other trig functions (cos, tan)?
Homework Statement
This is from a physics problem, but my question is more mathematically oriented.
After working through the problem, I arrive at the last step.
Sin(x)=.967
The question says that there are two possible angles for x.
The Attempt at a Solution
arcsin(.967)...
In my Trig class, we learned about the unit circle and its relationship to the various trig functions (sin, cos, etc.).
I am curious to know why the unit circle works the way it does, and the how it was "derived" so to speak.
More specifically, why does radius of the circle have to be 1 for...
A few days ago, I had a problem that looked like this:
evaluate cot(pi)
I know that on the unit circle, cot(pi) ends up as -1/0. In my precalc class, we say that this is undefined because you can't divide by zero.
I decided to plug the problem into wolfram and it tells me that there is...
Thank you very much!
I would never have thought of multiplying by (1/cos) because it seemed so...random, yet it works.
Do you have any tips on how to see things like that?
Homework Statement
Prove.
(sec(x)+1)/(tan(x))=(sin(x))/(1-cos(x))
Homework Equations
Trig Identities
The Attempt at a Solution
I decided to try and prove the identity by manipulating the function on the right side.
I multiplied both the numerator and denominator by...
I had a problem where we had to write out the sinusoidal function for the rotation of a ferris wheel. My teacher said that because the rotation was a function of time (x-axis was time), we had to use radians and not degrees.
Could someone explain to me if/why you need to use radian measurement...
Homework Statement
A charged particle, passing through a certain region of space,has a velocity whose magnitude and directions remain constant.
a. If it is known that the external magnetic field is zeroseverywhere in this region, can you conclude that the external electric field is also...