find the area of bounded by the two curves. y=9-x
Differential calculus is concerned with finding the slope of a curve at different points. Integral calculus is concerned with finding the area under a curve.
This is a calculus question. You would need to use an integral.
Integration can be used to calculate the area under a curve and the volume of solids of revolution.
The units of integral are typically expressed in square units, such as square meters or square inches. Integrals are used in mathematical calculations to find the area under a curve, the volume of a solid, or to solve various types of equations. They are a fundamental concept in calculus and are used to analyze and solve problems in a wide range of fields, including physics, engineering, and economics.
37.6
To solve problems that involve infinitesimal quantities. Such problems are solving for the slope of or area under a curve.
numbers, algebras, coordinate plane, geometry (shape, area, volume), calculus, theorems, and so on.
Calculus is a branch of mathematics which came from the thoughts of many different individuals. For example, the Greek scholar Archimedes (287-212 B.C.) calculated the areas and volumes of complex shapes. Isaac Newton further developed the notion of calculus. There are two branches of calculus which are: differential calculus and integral calculus. The former seeks to describe the magnitude of the instantaneous rate of change of a graph, this is called the derivative. For example: the derivative of a position vs. time graph is a velocity vs. time graph, this is because the rate of change of position is velocity. The latter seeks to describe the area covered by a graph and is called the integral. For example: the integral of a velocity vs. time graph is the total displacement. Calculus is useful because the world is rarely static; it is a dynamic and complex place. Calculus is used to model real-world situations, or to extrapolate the change of variables.
Calculus is mainly about limits, which in turn are used to calculate the slope of a line (known as the "derivative"; lots of applications for that), and to calculate the area under a curve (the "integral" - also lots of applications for that). For more details, read the Wikipedia article on "Calculus", or read an introductory book on calculus. As prerequisites, you should be well-acquainted with high-school algebra.
Its importance is tremendous - it has many different applications. Some of the applications include calculation of area, of volume, moment of inertia, of work, and many more.
The mathematical technique used to calculate the area under a graph is integral calculus. This is a complex subject which I am not going to attempt to explain in detail- it normally takes years of study.
To find the area under a graph, you can use calculus by integrating the function that represents the graph. This involves finding the definite integral of the function over the desired interval. The result of the integration will give you the area under the graph.