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when two molecules approach each other the charges in each are disturbed and redistributed in a fashion that the average distance among the unlike
when a spherical body goes by a viscous fluid it feels a viscous force the value of the viscous force increases with the enhance in speed of the
method of cylinders or method of shellsthe formula for the area in all of the cases will be
volumes of solids of revolution method of cylindersin the previous section we started looking at determine volumes of solids of revolution in
the property of liquids or gases by virtue of which a backward dragging force viscous drag acts tangentially on the layers of the liquid in motion
formulas for the volume of this solidv intba a x dx v intdc a y dywhere a x amp a y is the
some important issue of graphbefore moving on to the next example there are some important things to notefirstly in almost all problems a graph is
although it needs not concern us further we also consider that the flow is irrotational to check for this property let a tiny grain of dust goes with
viscosity in fluids is the analog of friction in solids both are methods by which the kinetic energy of moving bodies can be changed into thermal
the mean value theorem for integralsif f x is a continuous function on ab then there is a number c in ab such
average function valuethe first application of integrals which well see is the average value of a function the given fact tells us how to calculate
integrate followingint -2 24x 4- x2 1dxsolutionin this case the integrand is even amp the interval is accurate soint -2 24x 4- x2
even and odd functions this is the final topic that we have to discuss in this chapter firstly an even function is any function which
evaluate followingint 0ln 1 pi excos1-exdxsolutionthe limits are little unusual in this case however that will happen sometimes therefore dont
it explains that when an object is immersed partly or completely in a liquid it loses in weight similar to the weight of the liquid displaced by
the atmospheric pressure at any position is numerically similar to the weight of a column of air of unit cross-sectional area extending from that
there are really three various methods for doing such integralmethod 1this method uses a trig formula as intsinx cosx dx frac12 intsin2x dx -14
when an electron makes transition from higher energy level having energy e2n2 to a lower energy level having energy e1 n1 then a photon of frequency
constants of integrationunder this section we require to address a couple of sections about the constant of integration during most calculus class we
binding energy of a system is described as the energy released when its constituents are brought from infinity to form the system it can also be
types of infinity mostly the students have run across infinity at several points in previous time to a calculus class though when they have dealt
fundamental theorem of calculus part ii assume fx is a continuous function on ab and also assume that fx is any anti- derivative for fx henceaintb
fundamental theorem of calculus part iif fx is continuous on ab sogx aintx ft dtis continuous on ab and this is differentiable on a b and asgprimex
proof of if fx gt gx for a lt x lt b then aintb fx dx gt gxbecause we get fx ge gx then we knows that fx - gx ge 0 on a le x le b and therefore
proof of int fx gx dx int fx dx intgx dxit is also a very easy proof assume that fx is an anti-derivative of fx and that gx is an anti-derivative