Volume Under The Curve Math

Math help pweety pweese. Estimate the value for x 15. In this paper we present the real extension to the area under the roc curve in the form of the volume under the roc surface vus showing how to compute the polytope that corresponds to the absence of classifiers given only by the trivial classifiers to the best classifier and to whatever set of classifiers.

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Volume under the curve math. There are no answers yet. The volume of a sphere. Join yahoo answers and get 100 points today. Volume by rotating the area enclosed between 2 curves.

It is given that the the region r is bounded by the curve y tan 4 x the x axis and the line x pi 4. With these two examples out of the way we can now make a generalization about this method. The volume of the shape that is formed can be found using the formula. So the graph of the function y r2 x2is a semicircle.

Now let s give the two volume formulas. The equation x2 y2 r2represents the equation of a circle centred on the origin and with radius r. Area of d d da area of d d d a. Now imagine that a curve for example y x 2 is rotated around the x axis so that a solid is formed.

First the volume of the region e e is given by volume of e e dv volume of e e d v. Answer this question 100. Volume radius ftnction dx sum of vertical discs 2m x dx area from curve to x aris x dx area from line to x axis area of enclosed regon but the volume adds another dimension. Suppose f f is non negative and continuous on the interval a b.

Finding volume under curve. C find the y coordinates of the centroid of r. The volume is then v d c a y d y π 2 0 16 y 2 y 6 d y π 16 3 y 3 1 7 y 7 2 0 512 π 21 v c d a y d y π 0 2 16 y 2 y 6 d y π 16 3 y 3 1 7 y 7 0 2 512 π 21. Finally if the region e e can be defined as the region under the function z f x y z f x y and above the region d d in xy x y plane then volume of e d f x y da volume of e d f x y d a.

If we want to find the area under the curve y x 2 between x 0 and x 5 for example we simply integrate x 2 with limits 0 and 5. We rotate this curve between x r and x r about the x axis through 360 to form a sphere. B if r is rotated through 2pi about the x axis find the volume so obtained. V lim δx 0n 1 i 02πxif xi δx b a 2πxf x dx where v lim δ x 0 i 0 n 1 2 π x i f x i δ x a b 2 π x f x d x where.

Each segment in the area is rotated to form a disc circle 2m x dx x and the segments are the radii of all the discs in the solid x dx dx. Then the volume v v formed by rotating the area under the curve of f f about the y y axis is. If we have 2 curves y 2 and y 1 that enclose some area and we rotate that area around the x axis then the volume of the solid formed is given by. Rotation about the y axis.

What is the natural logarithmic regression equation for the following data. Volume pi int a b y 2 2 y 1 2 dx in the following general graph y 2 is above y 1. Please show me how to find the distance.