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The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 1/4x^2 - 1/2ln(x), 1 <= x <= 5 

          The given curve is rotated about the y-axis. Find the area of the resulting surface.
y = 1/4x^2 - 1/2ln(x), 1 <= x <= 5
The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 1/4x^2 - 1/2ln(x), 1 <= x <= 5

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 1/4x^2 - 1/2ln(x), 1 <= x <= 5
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Transcript

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00:01 Hi, in the given problem we are given with the curve y is equal to x square over 4 minus half ln x now this curve is between x less equal to 5 and greater equal to 1 so this curve is rotated about the y axis rotated about y axis so here in this case we get the solid shape whose surface area is to be found so, for that we will first find what is the y prime, which is dy over d x, so y prime is equal to 2 x over 2.
00:47 So that would be x over 2 minus 1 over 2 x.
00:56 Next, we will be using a definite integral in order to find the surface area...
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