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application of integral calculus in economics

application of integral calculus in economics

Let’s assume that the integration of a function ([latex]f(x)[/latex]) cannot be performed analytically. While differential calculus focuses on the curve itself, integral calculus concerns itself with the space or area under the curve.Integral calculus is used to figure the total size or value, such as lengths, areas, and volumes. Apply the ideas behind integration to economics and biology . The length [latex]s[/latex] of the part of the graph of [latex]f[/latex] between [latex]x = a[/latex] and [latex]x = b[/latex] can be found as follows. Types … This is an application of integral calculus, because it uses small droplets of water to determine the whole volume of water at any point in time. %�쏢 (adsbygoogle = window.adsbygoogle || []).push({}); Infinitesimal calculus provides us general formulas for the arc length of a curve and the surface area of a solid. Use the Taylor series to approximate an integral, Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function’s derivatives at a single point. Cost and revenue functions are calculated through indefinite integral. The definite integral can be used in a number of applications in business and economics. Pressure ([latex]p[/latex]) is force per unit area applied in a direction perpendicular to the surface of an object. ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 APC Maths INTRODUCTION: Quantitative techniques and mathematical models are now being increasingly used in business and economic problems. Therefore, the total flux [latex]F[/latex] is written as: [latex]\displaystyle{F = \int_{0}^{R} 2\pi r \, v(r) \, dr}[/latex]. Consider a swimming pool that is filled by water dripping from a tap. Click to Select (larger) image. With very little change we can find some areas between curves; indeed, the area between a curve and the x-axis may be interpreted as the area between the curve and a second “curve” with equation y = 0. Click to Select (larger) image. <> Volume 9. Integration . The standard normal distribution has probability density, [latex]\displaystyle{f(X;\mu,\sigma^2) = \frac{1}{\sigma\sqrt{2\pi}} e^{ -\frac{1}{2}\left(\frac{X-\mu}{\sigma}\right)^2 }}[/latex], This probability distribution has the mean and variance, denoted by [latex]\mu[/latex] and [latex]\sigma ^2[/latex], respectively. But, to answer the implicit question in the background, I don't think you should be too worried by this because: Economics involves a lot of fairly easy calculus rather than a little very hard calculus. Learning Outcomes Addressed in this Section. Now, calculate the surface area of the solid obtained by rotating [latex]f(x)[/latex] around the [latex]x[/latex]-axis: [latex]\displaystyle{A_x = \int_{0}^{1} 2\pi \sqrt{1-x^2}\cdot \sqrt{1+\left(\frac{-x}{\sqrt{1-x^2}}\right)^2} \, dx = 2\pi}[/latex]. Applications of the Derivative Integration Mean Value Theorems Monotone Functions Strictly Increasing Functions Example The function f : R !R de ned by f(x) = x3 is strictly increasing on R. The total flux of blood through a vessel with a radius [latex]R[/latex] can be expressed as [latex]F = \int_{0}^{R} 2\pi r \, v(r) \, dr[/latex], where [latex]v(r)[/latex] is the velocity of blood at [latex]r[/latex]. provided that [latex]x(t)[/latex] is never negative between the endpoints [latex]a[/latex] and [latex]b[/latex]. Cost of a commodity depends upon a number of factors. The two objects are rotating around their center of mass. For a continuous random variable [latex]X[/latex], the probability of [latex]X[/latex] to be in a range [latex][a,b][/latex] is given as: [latex]\displaystyle{P [a \leq X \leq b] = \int_a^b f(x) \, \mathrm{d}x}[/latex]. Set up two iterated integrals that represent the coordinates of the center of mass of the lamina.

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