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How To Find the Area Under a Graph with Integration?

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To Find the area under a curve can be done once you understand what integrals are, know the axis on the graph and the key role that constants play. Here are ways that will help you understand how to find the area under a graph with the process of integration. Integration helps you with solving equations and find the area under a graph. 

How To Find Area Under a Graph

The area under a graph is usually found by simple calculations. There are a few steps that we will take:

•The equation of the curve on graph (y=f(x)).

•Limits under which the area is being calculated and the axis with riemann sum calculator that closes the area.

•Find the antiderivative of the curve. 

•Add the upper limit and lower limit to the answer of integral and take the difference to find the area under the graph.

Equation To Find Area Under A Graph

Area = a∫by.dxa∫by.dx

       = a∫bf(x).dxa∫bf(x).dx

       =[g(x)]ba[g(x)]ab

       =g(b)−g(a)g(b)−g(a) 

The Method Of Integration 

One of the methods to find the area under a graph is the method of using integration. Integration is also worded as antiderivative is also known as Integration. In this method we require the equation that will help us find the area under the graph for the curve. The area can be found through calculating in accordance with the axis. The axis are denoted as x-axis and y-axis. 

Using Calculators

One way to solve mathematical problems is always made easy through calculating with the help of riemann sum calculator.

For find the area under a graph we can take an easy route by using a riemann sum calculator. The equation of Riemann Sum is: S=∑i=1nf(xi∗)Δx

The Riemann Sum helps us with approximation. It gives a step by step process within seconds.

Left Riemann Sum formula helps with estimating the functions of the given values on the left endpoint. It provides with the height and base of several rectangles and gives the formula:

ALeft=Δx[f(a)+f(a+Δx)+…+f(b+Δx)]

The Right Riemann Sum formula estimates the value on the right endpoint. This provides the base height f(a + iΔx) and Δx. The formula we get from Right Riemann Sum is:

ARight=Δx[f(a+Δx)+f(a+2Δx)…+f(b)]

Finding Of Area Depends Upon The Situation Provided 

The integration method also depends upon the cases that have been provided. It is important to know the situation and then apply the formulas and equations accordingly. For curves which are entirely above the x axis we are to use Area=∫ab​f(x)dx to find the area. For finding area under a curve from the very first principle we use Area=∫ab​f(x)dx to find the area. These are followed by the Riemann Sum formulas. For instance if the curves are entirely below the x axis we will use Area=∣​∫ab​f(x)dx ∣​. If we get a part of a curve below the x axis and part of it above the x axis, we will use the formula Area=∣​∫ac​f(x)dx∣+∫cb​f(x)dx. 

Finding the area under a graph depends upon the situations that are provided. The axis of the graph plays a huge role. These axis indicate how and what formula is supposed to be used according to the provided situations.

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