Area Under The Curve Calculator

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Introduction to the Area Under the Curve Calculator

To find tha area under the curve you must need to know about the concepts of integrals. However which technique of integral requires to answer that how to find area under the curve? That a question that triggers when you think to solve for integral of irrgeular shaped body. But here the curve area integral calculator which provide an accurate estimate of the area of a specific region under the curve.

The area under graph calculator is an online tool for evaluating the area. This online integral tool displays the area for the given curve function with defined limits in a few seconds. The area under the curve calculator makes the calculation faster and more accurate. The area under two curves calculator calculates the risk-free and understandable calculations.

Beside to this, also find integral using trig substitution calculator and integral u substitution calculator, if you find hard to solve integration by u substitution method.

What is Area Under Curve Calculator?

An integral area calculator is a tool that uses the method to calculate the area of definite integrals between upper and lower limits. Basically, the area under the integral curve calculator is used for finding the areas of irregular figures.

area under the curve calculator

This calculator will helps you for solving the long division, equations and provide you faster and acurate results.

Formula Used by Integral Area Calculator

The area under two curves calculator calculates definite integrals with step-by-step instructions. This calculator uses the following formula with step-by-step instructions to solve the improper integral problems:

Here

a & b are upper and lower limits

F(x) is the given curve function.

The above formula is used by our area under 2 curves calculator to calculate the area under the curve by using the integration method.

How to Find Area Under the Curve?

Example : Find the total area between the curve y = x3 and the x-axis between x = -2 to x = 2.

Solution: If we simply integrate x3 between -2 to 2, we will get:

$$ \int_{-2}^2 x^3 dx \;=\; \frac{x^4}{4} \biggr|_{-2}^{2} \;=\; 4-4 \;=\; 0 $$

So, instead of splitting the graph, we will split the integral into two

$$ \int_{0}^2 x^3 dx \;=\; \frac{x^4}{4} \biggr|_{0}^{2} \;=\; \frac{16}{4}-0 \;=\; 4 $$ $$ \int_{-2}^0 x^3 dx \;=\; \frac{x^4}{4} \biggr|_{-2}^0 \;=\; 0 - \frac{16}{4} \;=\; -4 $$

So the area is 4.

When we add these two splitted integrals, we will get area under the graph as 8 units.

How to Use Area Under Graph Calculator?

An area under curve calculator with steps finds the area under the curve with the integration by following these guidelines

Input:

  • Enter your curve function or Load example.
  • Now, Enter the upper and lower limits.
  • Then, select the variable for integration from the given list.
  • Finally click on the "CALCULATE" button to find the area under the curve.

Output:

On the result page, this integral area calculator will provide:

  • The visual representation of the integral function.
  • The area of the specific region with all possible intermediate steps.

How to Get this Area Integral Calculator Online?

The following steps are followed to find the area under the curve calculator with steps:

Step 1: First of all, enter the keywords in the search bar.

Step 2: Google shows you some suggestions for the searched calculators.

Step 3: Now select the Integral Calculator from Google suggestions

Step 4: Then choose this calculator for the area under curve calculator is displayed on your screen.

For lengthy and complex integral calculation, use our integration by partial fraction calculator as well as integration by parts step by step calculator. These will save your time and efforts while solving complex integration methods.

Benefits of Calculator for the Area Under the Curve

The area of the region under the curve calculator has the following benefits:

  • The area under the curve integral calculator will calculate the problems in just a few minutes and solve the curve functions step-by-step.
  • It is a time-saving tool for solving the area of irregular figures and shapes.
  • It keeps you away from complex and hectic manual calculations.
  • This online calculator provides free of cost solution without demanding any cost.
  • The area under 2 curves calculator evaluates the area of different definite and indefinite functions.
  • The area under the graph calculator gives you the results in the form of graphs, possible intermediate steps, real and imaginary parts and alternatwe form of definite and indefinite integrals.
  • The results of the area integral calculator are fast, accurate and reliable.
  • The area under the curve calculator with steps gives you accurate and authentic results.

So this is all about integral curve area calculator. For more online tools and learning guides, stay tuned with us.

Frequently Asked Question

What does the Area Under the Curve Represent?

The area under the curve is used in different fields and it represents the quantitative measure of something that varies continuously over the integral. Let’s break down in a few different contexts:

In calculus, the area under the curve represents the integral of the function. If there is a function and a graph is plotted then the area under the curve from x = a to x = b represents the definite integral of f(x) over the integral.

While dealing with probability density functions the area under the curve represents probabilities. Especially, if probability density functions are integrated from a to b then the results give the probability that a random variable falls in that range.

If dealing with standard normal distribution then the area under the curve helps to find out probabilities related to z scores. The area under a curve calculator can help you solve it all.

The use of the area under the curve concept is in the context of receiver operating characteristics curves which is used to calculate the performance of the binary classifiers. The area under the curve represents the probability in which the randomly chosen positive instance is ranked higher than the randomly chosen negative instance.

In pharmacokinetics, the area under the curve represents the total exposure to a drug after administration. It measures the amount of drug in the blood stream.

What is Area Under the Curve?

The area under the curve refers to as the area enclosed between the curve and the baseline within the specified range. In the area under the curve, the definite integral function is a bounded curve above or below the region along the x-axis.

How to Estimate the Area Under a Curve

There are different methods to estimate the area under the curve depending on the context and the level of precision that is required. It is possible to solve such problems using the graph area calculator but there are techniques and those common techniques for estimating the area under the curve is given below,

  • The first technique is to use the integration. If the function representing the known curve and the curve is integrable as well then the most accurate way is to calculate the definite integral.
  • If the function is complex and needs a computational solution then the numerical method can approximate the area under the curve. In it, the common techniques are the trapezoidal rule, Simpson's rule, and Monte Carlo simulation.
  • If the curve forms a simple geometric shape then the area can be estimated by determining the area of the shapes and adding them up.
  • If there is no analytical representation of the curve but has the data points then the data can be plotted on graph paper and the use of counting or graphical tools to estimate the area.

What is the Total Area Under a Normal Curve

The total area under a normal curve is known as the standard normal distribution or Gaussian distribution which is exactly 1 and not more than that.

The normal curve is the bell-shaped curve that describes the distribution of variables in the population. A property of the normal curve is that the area under the curve represents the probabilities and the total area must add to 1.

For the standard normal distribution, the area under the curve can be determined by integrating the probability over its entire range. The probability density function as per the area of region calculator for the standard normal distribution is given below as,

$$ \frac{1}{\sqrt{2 \pi}} exp \biggr( - \frac{x^2}{2} \biggr) $$

Can Area Under the Curve be Negative

The area under the curve can be or cannot be negative depending on the situation. The area under the curve is generally associated with a non-negative value as it represents the total measure such as probability, accumulated quantity, or magnitude.

But there are some scenarios where the area under the curve can be interpreted as negative depending on the context,

In calculus, the area under the curve is referred to as the definite integral. While integrating a function over a range, whenever the curve is below the x-axis then the integral will have a negative value. In the area of curve calculator, The negativity represents the accounting for the positive and negative regions and the net accumulation.

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