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What is the volume of the solid when the region bounded by Y 4 x2 and Y 0 is revolved about the x axis?
The volume is 107.233 .
How do you find the volume of a solid revolved around the Y-axis?
Answer: The volume of a solid rotated about the y-axis can be calculated by V = π∫dc[f(y)]2dy. Let us go through the explanation to understand better. The disk method is predominantly used when we rotate any particular curve around the x or y-axis.
How do you find area and volume in calculus?
The volume of each shell is approximately given by the lateral surface area 2π⋅radius⋅height multiplied by the thickness: 2πx[2x−x2]dx.
What is the volume of Revolution V for the positive x region?
There are 2 possible regions, depending on whether x is positive or negative. The curves y = 3 – x^2 and y = 2^x intersect at 2 points, (1, 2) and approximately (- 1.64, 0.32). The exact values would be transcendental. I have evaluated the volume of revolution V for the positive x region. The integral is or approx. 24.37 cubic units.
How many possible regions does x = 3 – x^2?
There are 2 possible regions, depending on whether x is positive or negative. The curves y = 3 – x^2 and y = 2^x intersect at 2 points, (1, 2) and approximately (- 1.64, 0.32). The exact values would be transcendental.
How do you calculate volume from shell method?
The Shell Method (about the y-axis) The volume of the solid generated by revolving about the y-axis the region between the x-axis and the graph of a continuous function y = f (x), a ≤ x ≤ b is b a b a V 2π[radius] [shellheight]dx 2π xf (x)dx Similarly,
How to calculate volume of solid generated by revolving?
(Shell Method, about the line x = k, i.e., a line parallel to the y-axis) The volume of the solid generated by revolving about the line x = k the region between the graphs of continuous functions y = F(x) and y = f (x), F(x) ≥ f (x), a ≤ x ≤ b, k not between a and b, is
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