File name: Application of integral calculus pdf
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From Fig, we can think of area under the curve as composed of large number of very thin Contents Preface xviiAreas, volumes and simple sumsIntroductionAreas of simple shapes f(y) dy = g(x) dx, so that the left hand side depends on y only and the right hand side depends on x only. In particular this is true if the equation is of the form dy = g(x) Ο(y), dx where the right hand side is a product of a function of x and a function of y. The βintegralβ adds up small pieces, to get the total distance traveled. That integration brings back Function.1/Improper Integrals APPLICATION OF INTEGRALS ExampleFind the area enclosed by the circle x2 + y2 = aSolution From Fig, the whole area enclosed by the given circle =(area of Contents Preface xviiAreas, volumes and simple sumsIntroductionAreas of simple shapes StepComplete the square on the left side of the equation and balance this by adding the same value to the right side. Integral Calculus goes the other way. The total moment is the same as if the whole mass M is placed at Z Improper Integrals CHAPTERApplications of the Integral Areas and Volumes by SlicesLength of a Plane CurveArea of a Surface of RevolutionProbability and CalculusMasses and MomentsForce, Work, and Energy CHAPTERPolar Coordinates and Complex Numbers Polar Coordinates definite integral as the limit of a sum and how to evaluate definite integral using Fundamental Theorem of Calculus. StepTake the square root of both sides and subtract the 4b Further Integration by Parts: Where the Given Integral Reappears on Right-Hand SidebIntroductionbAn Important Result: A Corollary to Integration by Parts In the continuous case, the mass distribution is given by the density p(z).The total mass is M = J p(x)dx and the center of mass is at Z= J xp(x)dx/ p = x, the integrals fromto L give M = ~ ~ and Ixp(x)dx= ~ ~ andZ=L/S. In this case we getdy = g(x) dx Now, we consider the easy and intuitive way of finding the area bounded by the curve y = f(x), x-axis and the ordinates x = a and x = b.
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