Recent content by insane0hflex

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    An integral by parts problem - please advise

    Homework Statement The function is increasing and has a inverse f^-1 Also assume f′is continuous and f'(x) > 0 over the state interval of integration [a,b] PLEASE NOTE! a is lower limit, b is upper limit (same for alpha and beta symbol later on) Used integration by parts to show that: \int...
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    Need help trying to integrate a messy function

    Thank you, worked it out and will ask the professor tomorrow. Thanks for your help!
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    Need help trying to integrate a messy function

    Homework Statement Evaulate the following integral: 2*integral from r-b to r of h(x-r+b)b*sqrt(r2-x2) dx or a picture http://imgur.com/n2PUN Homework Equations The Attempt at a Solution Tried setting u = r^2-x^2, lost after a couple more steps. Nothing seems to cancel out smoothly. For the...
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    Volume of cathedral dome (Using volumes of revolution, disk method)

    Okay, that helps a little bit. So I would derive an expression for the area of the base, then take the integral from 0 to h? (since h = r correct)?
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    Integral of 1/sqrt(u^2-a^2) du, when u < -a

    Homework Statement Show and prove that where u < -a: integral of 1/(sqrt(u^2-a^2)) = ln(u+sqrt(u^2-a^2))+C or -cosh^-1(-u/a)+C Homework Equations when u > a, the integral of 1/(sqrt(u^2-a^2)) = ln(u+sqrt(u^2-a^2))+C or -cosh^-1(-u/a)+C My attempt at a solution: Don't I just use the same...
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    Volume of cathedral dome (Using volumes of revolution, disk method)

    Homework Statement A cathedral dome is designed with three semi circular supports of radius r so that each horiontal cross section is a regular hexagon. Show that the volume of the dome is r^3 * sqrt(3) an accompanying figure - http://imgur.com/3fSqh Homework Equations...
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    Calculus - limit with f(x) and g^2(x) in limit

    Homework Statement See the bottom problem (#2) See image - http://imageshack.us/photo/my-images/842/img7774y.jpg/ The Attempt at a Solution Plugged in 2 for f(x) and -4^2 for g^2(x) got 2/3, Is this correct? All help appreciated! Mad at my Calc teacher because he never gave us...