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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

    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

    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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    Particle Behavior in Double Slit

    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...
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    How accurate is this video? Double Slit experiment

    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...
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    How do you prove this Trig identity?

    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...
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    How hard is Probability?

    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...
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    Finding the inverse of Sin

    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)...
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    Why does the Unit Circle work?

    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...
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    Dividing by Zero=undefined or complex infinite?

    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...
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    (sec(x)+1)/tan(x) = (sin(x))/(1-cos(x))

    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...
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    Why do we use Radian measurement for Time?

    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...
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    Magnetic Field and electric Field

    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...
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    Euler's Formula and Complex Logarithms relationship

    I've become rather curious, as of late, about the realm of complex logarthims; more specifially logarithms in the form log(z) where z is any negative number. Excuse any ignorance on my part, as I'm only in Precalculus, but I was just curious to see how Euler's formula is related to complex...
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    Defining negative logarithms

    I recently had a test (precalc) where we had to solve log(x)-log(x+4)=2 for x. The answer comes out negative. I understand that in precalc we are defining the logarithms for just positive numbers, but- Is it ever justified to define a logarithm for all numbers, both negative and...
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    Time changing

    Hello, How would I change my time settings? It's annoying to find out when people posted something when the time is wrong. Thanks
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    Log(x)-log(x+4)=2 discrepancy

    Homework Statement log(x)-log(x+4)=2 Homework Equations knowledge of logs The Attempt at a Solution This question was on a test, and I found the answer to be approximately -400/99. I was marked off, because apparently the answer is no solution? I checked wolframalpha, and they...
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    Solve e^(2 x)-e^x-12 = 0 for x

    Homework Statement solve e^(2 x)-e^x-12 = 0 for x Homework Equations quadratic The Attempt at a Solution We had this question on a test, and after solving it (i'd rather not write out the work), I came to two solutions. Ln(4) Ln(-3) I plugged both answers back into the...
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    Origin of rms speed

    We've just learned about kinetic theory and gases and my teacher showed us the rms speed. He himself doesn't know why its called the rms speed, or how it originated and I was curious to find out myself. Why go through all the trouble when you could just say the average speed? If anyone could...
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    How to enter equations

    Hello guys, I still getting used to these Forums, and I've seen people post responses with "neater" equations. Is there a way to enter in numbers, exponents and other symbols neatly instead of having to write them out. ex. sqrt(9)=3 Thanks
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    E^x+x = 5

    Homework Statement e^x+x=5 Homework Equations Lambert W-function? The Attempt at a Solution I moved everything around and got: Ln(5-x)=5.... It doesn't really help. I looked at wolframalpha, and it said I need the Lambert W-function (no clue what that is). Can this...
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    Speed of water and height involving fluid mechanics

    Homework Statement In a very large closed tank, the absolute pressure of the air above the water is 6.01x10^5 Pa. The water leaves the bottom of the tank through a nozzle that is directed straight upward. The opening of the nozzle is 4.00m below the surface of the water. a) Find the speed at...
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    Absolute pressure with container

    Homework Statement A 1.00m tall container is filled to the brim, partway with mercury and the rest of the way with water. The container is open to the amosphere. What must be the depth of the mercury so that the absolute pressure on the bottom of the container is twice the atmospheric...
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    V^2 − (v/4)^2 = 196

    Homework Statement I'm solving for v in: v^2 − (v/4)^2 = 196 Homework Equations The Attempt at a Solution →v^2(1-(1/4))=196 →v^2(.75)=196 → √(196/.75)≈16.17 What did I do wrong? I know this isn't the right answer, but why?
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    3^x = 12x-9

    Homework Statement 3^x=12x-9 Homework Equations The Attempt at a Solution I really have no clue how to solve this one algebraically. I graphed the two functions on a calculator and found the points of intersection the answers are 3 and 1 Can someone show me how to solve...
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    Calculus: an intuitive and physical approach

    I'm currently enrolled in precalculus and I'm finding that almost everything we've learned so far is just Algebra 2 review. I've been looking for a book where I can self study Calculus and move ahead, and I stumbled upon Calculus: an intuitive and physical approach by Morris Kline. I am...
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    Crate being pulled at angle, find tension

    Hello, I'm new to physics forums, so excuse me ahead of time if something is wrong. Homework Statement A warehouse employee drags a 72 kg wooden crate across the floor at a constant velocity by pulling on a strap attached to the bottom of the box. The crate is tiled 25° above the...