# Beginner Integration: Intg'g Arbitrary Funcs: Area B/w Intersects

• Jake Minneman
In summary, the conversation discusses the definition of an integral in the form of ∫a to b f(x)dx=F(b)-F(a) and the use of integration to calculate the area between two intersecting functions. It is suggested to do two integrations, one for each function when it is underneath.
Jake Minneman
http://www.google.com/imgres?imgurl=http://www.msstate.edu/dept/abelc/math/integral_area.png&imgrefurl=http://www.msstate.edu/dept/abelc/math/integrals.html&usg=__eYIUnirereMFeYOxrfWSZ22D6MU=&h=599&w=684&sz=24&hl=en&start=0&sig2=5Xoc8E51gnWrd4Z6mnluLA&zoom=1&tbnid=ofF46QkIclKjQM:&tbnh=142&tbnw=162&ei=7VfZTbHvDdO_gQfe49lX&prev=/search%3Fq%3Ddefinition%2Bof%2Ban%2Bintegral%26um%3D1%26hl%3Den%26sa%3DN%26biw%3D1416%26bih%3D1071%26tbm%3Disch&um=1&itbs=1&iact=rc&dur=520&sqi=2&page=1&ndsp=44&ved=1t:429,r:22,s:0&tx=106&ty=50
I know this to be the definition of an integral in the form of
$$∫a to b f(x)dx=F(b)-F(a)$$
But what if, however, there were another arbitrary function intersecting the function in the picture twice each with a curved nature. For example the function sin(x) is it possible buy using integration to calculate the area in between the two intersection points and the x-axis
Kind of a strange question, and its not very to the point ask questions if you do not understand my wording.

Hi Jake!

You mean the area under the lower of two intersecting functions?

Just do two integrations, one for the first function when it's underneath, the other for the second function when it's underneath.

Yes exactly, thank you very much.

## 1. What is integration?

Integration is a mathematical concept that involves finding the area under a curve on a graph. It is the inverse operation of differentiation, which involves finding the slope of a curve at a given point.

## 2. What is the purpose of integrating arbitrary functions?

The purpose of integrating arbitrary functions is to find the area between the curve and the x-axis, which can be used to solve various real-world problems related to distance, velocity, and acceleration.

## 3. How do you integrate arbitrary functions?

To integrate an arbitrary function, you must first determine the limits of integration, which are the starting and ending points of the area under the curve. Then, you can use various integration techniques, such as substitution, integration by parts, or trigonometric substitution, to find the antiderivative of the function and solve for the area.

## 4. What is the relationship between integration and differentiation?

Integration and differentiation are inverse operations of each other. This means that if you integrate a function and then differentiate the result, you will get back to the original function. Similarly, if you differentiate a function and then integrate the result, you will also get back to the original function.

## 5. Why is it important to find the area between intersects of arbitrary functions?

Finding the area between intersects of arbitrary functions is important because it allows us to solve various real-world problems, such as calculating the displacement of an object given its velocity over time or determining the work done by a variable force. Additionally, it is a fundamental concept in calculus and is used in many fields, including physics, engineering, and economics.

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