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mannaatsb
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i've been stuck on this problem for an hour now. how do you find the surface area for y=(x)^1/2 when 0_<x_<2, rotating about the x axis?
The formula for finding the surface area of y=(x)^1/2 rotating about the x axis is ∫2πyds, where y=(x)^1/2 and ds is the arc length element.
To set up the integral, first find the arc length element ds by using the formula ds=√(1+(dy/dx)^2)dx. Then, substitute y=(x)^1/2 into the formula and integrate from the limits of the curve.
Surface area of rotation is the measure of the total area that is created when a curve is rotated around a given axis. This concept is commonly used in mathematics and physics to find the surface area of a three-dimensional object.
The difference between finding surface area of rotation and finding volume of rotation is that surface area measures the total area of the curved surface, while volume measures the space enclosed by the curved surface. Surface area uses the arc length element ds, while volume uses the area element dA.
Yes, the formula for finding surface area of rotation can be applied to any curve as long as the curve is rotated around a given axis. However, the integral may become more complex for more complicated curves.