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...