Recent content by californicate

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    Volume of Solid of Revolution for y=x^2-2, y=0 about y=-1

    It's radius is 1, so it's circumference is 2pi. It's length is 2x, so 2sqrt(y+2)?
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    Volume of Solid of Revolution for y=x^2-2, y=0 about y=-1

    We didn't use terms like by shells and by cylinders in lecture so I'm trying to follow along, but since if I'm doing by cylinders would I then require the constant to be 2pi?
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    Volume of Solid of Revolution for y=x^2-2, y=0 about y=-1

    So, if integrating in terms of y, I would integrate x=sqrt(y+2) from -1 to 0?, So my final integral is pi (integral from -1 to 0) (sqrt(y+2))^2 dy?
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    Volume of Solid of Revolution for y=x^2-2, y=0 about y=-1

    Homework Statement Find the volume of the solid of revolution obtained by rotating the area bounded by the curves about the line indicated. y=x2-2, y=0 about y=-1. Need only consider part above y=-1 Homework Equations V=∏a∫b[f(x)]2dx The Attempt at a Solution I'm mainly unsure of...
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    Minimizing area of a semicircle bounded by two lines

    I'm thinking I should only consider the integral of one half and then double it, as it is symmetrical. I know the total range of x is from 0 to 1. I'll have to integrate this in two parts as the upper and lower function alternate. The first would be the integral from 0 to the meeting point of...
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    Minimizing area of a semicircle bounded by two lines

    So the range of y above the line is from a(the line) to 1 The value of x is -√1-y2, if it's to the left of the origin at the midpoint. If I integrate in terms of x, say, I have the integral from 0 to some point of (equation of circle - a) + the integral from that same point to 1 of...
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    Minimizing area of a semicircle bounded by two lines

    It states in the question the radius of the circle is 1, not a, and so x^2 + y^2 =1 and so x=sqrt(1-y^2)
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    Minimizing area of a semicircle bounded by two lines

    It appears the image link did not work, here it is again: http://imgur.com/grrCqWF
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    Minimizing area of a semicircle bounded by two lines

    Homework Statement The figure shows a semicircle with radius 1, horizontal diameter , and tangent lines at and . At what height above the diameter should the horizontal line be placed so as to minimize the shaded area http://imgur.com/grrCqWF Homework Equations The equation of a...
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    What is the surface area when a curve is rotated about the x-axis?

    So should the x inside the integral be replaced with an f(x)? That's the equation the prof gave in class, however in examples he switched back and forth between using f(x) and x. I'll ask about it next class. Thanks!
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    What is the surface area when a curve is rotated about the x-axis?

    Homework Statement Obtain the surface area when the curve y=ex, 0≤x≤1, is rotated about the x-axis Homework Equations Surface Area = 2∏a∫b x√(1+(dy/dx)2)dx The Attempt at a Solution I started with the the equation, Surface Area = 2∏0∫1 x√(1+e2x)dx. However, whichever way I try to...
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    Calculus 2 second derivative of integral

    Homework Statement Find d2/dx2 0∫x (1∫sint√(1+u^4)du)dtHomework Equations The Attempt at a Solution Initially I treated this problem as the second derivative of a double integral and thus quickly found myself at the result cosx√1+sin4x, by the fundamental theorem of calculus. However I...