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    Definite Integral of Absolute Value Function (Calc I)

    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!
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    Definite Integral of Absolute Value Function (Calc I)

    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...
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    Integrate sqrt(9-x^2) by hand

    Alright then, I guess that's something I'll have to study later on. Thanks!
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    Integrate sqrt(9-x^2) by hand

    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!
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    Integrate sqrt(9-x^2) by hand

    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...
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    X^3-2x-2cos(x) find local extrema

    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...
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    Dy/dx of arcsin(1/x^4) clarifying question

    Thanks for all your help Simon (and others)! I think I'll rest with the fact that it's something to do with WolfRam's programming.
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    Dy/dx of arcsin(1/x^4) clarifying question

    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...
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    Dy/dx of arcsin(1/x^4) clarifying question

    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...
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    Dy/dx of arcsin(1/x^4) clarifying question

    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...
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    Dy/dx of arcsin(1/x^4) clarifying question

    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}##?
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    Dy/dx of arcsin(1/x^4) clarifying question

    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.
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    Dy/dx of arcsin(1/x^4) clarifying question

    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...
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