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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
proof of various integral factsformulaspropertiesin this section weve found the proof of several of the properties we saw in the integrals section
rolles theorem assume fx is a function which satisfies all of the following1 fx is continuous in the closed interval ab2 fx is differentiable in
fermats theorem if fx has a relative extrema at x c and fprimec exists then x c is a critical point of fx actually this will be a critical point
proof of limqrarr0 cosq -1q 0we will begin by doing the followinglimqrarr0 cosq -1q limqrarr0cosq - 1cosq 1q cosq 1 limqrarr0cos2q - 1 q cosq
in x-ray tube when high speed electrons strike the target they move into the target they lose their kinetic energy and come to rest inside the solid
i x-rays are electromagnetic waves with wavelength lie among 01aring - 100aringii x-rays is invisibleiii they always go in a straight line
depending upon the penetration power there are two parts of x-rayshard x-raysmore penetration powermore frequency of the order of asymp 1019 hzlesser
chain rule if fx and gx are both differentiable functions and we describe fx f gx so the derivative of fx is fprimex f primegx
quotient rule fg fg - fgg2here we can do this by using the definition of the derivative or along with logarithmic definitionproof here we do the
x-rays was discovered by scientist rontgen thats why they are also known as rontgen pulsesrontgen discovered that when pressure inside a discharge