|Subject||Mathematics – ENG|
|Chapter||VIII – Application of Integrals|
Application of Integrals – Introduction
In geometry, we have learnt formulas to calculate the areas of various geometric shapes, including triangles, rectangles, trapeziums, and circles. Such formulas are fundamental in the applications of mathematics for many real-life problems. The formulas of primary geometry allow us to calculate the areas of many simple shapes. However, they are insufficient to calculate areas surrounded by curves. For that, we will need some concepts of integral calculus.
In the previous chapter, we have studied to find the area surrounded by curved y = f (x), coordinate x = a, x = b, and x-axis, calculating the exact integral as the limit of yoga. Here, in this chapter, we will study the specific application of integrations to determine the area under simple curves, the area between the circles, the parabola, and the lines and arcs of the ellipse (standard form only). We will also talk about finding an area surrounded by the above curves.