Recent content by winston2020

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    Learn How to Factor Quadratics: Step-by-Step Guide for Gr. 10 Math Homework

    Homework Statement Factor. 2x^{2}+5x-12 I just took a semester off from school and I feel dumb. My recommendation to anyone reading is don't do that. Anyways, back to gr. 10 math :cry: Normally if I was going to factor this I would try to eliminate the coefficient of x^{2} but it...
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    Integrating cos(px) from 1 to 2 with a constant p

    Ok, should it go something like this?: \int_{1}^2cos(px)dx Let u = px Therefore, du = pdx And, dx = \frac{du}{p} So, \int_{1}^2cos(px)dx = \int_{1}^2cos(u)\frac{du}{p} = \frac{sin(u)}{p} + c Is that correct?
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    Differentiating sin^2[3x]: Chain & Product Rules

    Thank you :smile:
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    Differentiating sin^2[3x]: Chain & Product Rules

    Exactly. So then this is my logic: Since sin^2(u) = [sin(u)]^2 Let u = 3x And let v = sin(u) i.e. \frac{d}{dx}v^2 = 2v = 2(sin(u)) * \frac{d}{dx}sin(u) = 2(sin(3x)) * cos(3x) * \frac{d}{dx}3x = 2(sin(3x)) * cos(3x) * 3 = 6(sin(3x)cos(3x)) And since...
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    Integrating cos(px) from 1 to 2 with a constant p

    Not really... what is du = pdx? du is the same as \frac{d}{dx}u right? But why is that useful? And what is pdx?
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    Integrating cos(px) from 1 to 2 with a constant p

    Homework Statement Solve the following Integral: \int_{1}^2cos(px)dx where p is a constantHomework Equations The Attempt at a Solution I'm totally lost here...
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    Integrate 4x^2+2: Solve for x=3 to x=1 - 44/3

    Cool thanks. Could you check out this https://www.physicsforums.com/showthread.php?t=256875" again?
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    Differentiating sin^2[3x]: Chain & Product Rules

    Oh man, I really over complicated things. Thanks :D EDIT: Wait though... shouldn't sin switch to cos at some point? Doesn't the chain rule mean it should go something like this: = 2sin(3x)*cos(3x)*3 = 6* sin(3x)cos(3x) = 3( 2sin(3x)cos(3x) ) = 3( sin(2 *3x) ) = 3sin(6x)
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    Integrate 4x^2+2: Solve for x=3 to x=1 - 44/3

    Awesome! My morale just sky rocketed... By the way, sorry for the bad latex graphic thing... I'm having a hard time figuring that out.
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    Integrate 4x^2+2: Solve for x=3 to x=1 - 44/3

    Hi, I've got to solve for: \int\stackrel{3}{1}(4x2+2)dx This is what I've done: = [ (4/3)x3 + 2x ]\stackrel{3}{1} = [ (4/3)(3)3 + 2(3) ] - [ (4/3)(1)3 + 2(1) ] then I solved... = 44/3 Is that correct at all?
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    Differentiating sin^2[3x]: Chain & Product Rules

    I'm not sure how to differentiate sin^2[3x]. Although, I think it's just d/dx( (sin[3x])(sin[3x]) ). So, just chain and product rules should do it. Is that right? EDIT: I've followed through with the above method, and I got 3*sin(6x). Is that correct?
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    Area under y=x^2: Calculate the Antiderivative

    Thanks everyone. I actually do understand how to get this particular example's anitderivative. I wanted to know if there was a more general way of achieving this. I can only imagine once f(x) gets a little more complicated, finding the antiderivative could get quite painful (although finding...
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    Area under y=x^2: Calculate the Antiderivative

    This is out of my textbook: EXAMPLE 6: Find the area under the parabola y=x2 from 0 to 1. SOLUTION: An antiderivative of f(x) = x2 is F(x) = 1/3x3. The required area is found using Part 2 of the Fundamental Theorem... My question is: how was the antiderivative obtained?
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    How to use derivatives and integrals

    It's nothing to do with me; even my professors and TAs have said it's a problem with the high school curriculum. They no longer sufficiently prepare students for university... one of the most lacking subjects apparently is math. With that said, thank you all for your advice. I am enrolled...
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