Integration Assignment Example | Topics and Well Written Essays - 750 words - 1

Integration - Assignment ExampleThe modern practice in schooldays curriculum is that instructors teach differentiation first before integration in contrast to the inception of tartar (Pitt, 2012).In the 17th century, Newton and Leibniz contribution made a milestone in advance of scientific developments in Europe. Kepler found the volume of a bucket of wine to be a pile of comminuted horizontal circular discs. B. Cava pillowris line formed from many points, plane formed from many lines and lusty made from many planes. All these gave initiating ideas in integration. At the same time Newton and Leibniz related integration and differentiation to be reverse processes in their Fundamental Theorem of Calculus popularly known as Newton-Leibniz saying (Stewart, 2010).The calculus method became a very powerful tool in solving mathematical problems where otherwise analytical methods failed those times. For instance, Jacob Bernoulli use calculus methods discovered that logarithmic spring under various transformations is invariant. In 1696, Johann Bernoulli asked a question that said, assuming friction was zero the path clutchn by a point concourse to slide from a point that is higher to a point that is lower taking the shortest time viable (Hawkins, 2001). This led to the development of the calculus of variation. Other 17th century developments are contained in Eulers gate in analysis infinitorum, institutiones calculi differentialis and institutions calculi Integralis.Consider the following shape, to find the volume and the surface area of the shape using integration then employ the use of infinitesimally small areas and volumes. Obtain the volume using this formulaFor example, take a parabola in the x-y plane whose height bases on another parabolic function. Say, from x=-2 to x=2 that has elevation determined by a circle of radius 4 i.e. . Taking y to lie between y=x2+4 and y=12-x2 then the volume is given byIntegrating once again using