Area Under The Curve Calculator

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Enter a Function:

Upper Limit: (inf = ∞ , pi = π)

Lower Limit: (inf = ∞ , pi = π)

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what's area beneath the Curve (AUC)?

In arithmetic, the area under the curve for the given feature f(x) having the bounds x = a and x = b is given through the particular quintessential formula. In case, if the vicinity among bounding values lies above the x-axis, then it has a high-quality signal. If the place among two values lies below the x-axis, then the negative sign has to be taken.

The place beneath a curve between two factors is discovered out by means of doing a exact vital between the two factors. To discover area underneath curve y = f(x) among x = a & x = b, you need to integrate y = f(x) among the bounds of a and b. This region may be calculated the usage of integration with given limits.

Calculate vicinity below Curve:

The place underneath a given characteristic has an higher restriction and a lower restriction, that are decided through the integrations. in an effort to find place under the curve by means of hand, you have to keep on with the following step-by way of-step recommendations:

Take any function f(x) and restrict x = m, x = n
carry out integration on the characteristic with higher limit n and decrease limit m.
Calculate the points and enter the values a and b.
Subtract f(n) from f(m) to gain the outcomes.

However, if you want to do danger-free calculations, then place beneath the curve calculator discover the region in a fragment of a 2nd.

Example

Calculate the area under the curve $ y = 2x^2 + 3 $ with limits $x = 1$ to $x = 2$?

Solution:

Given function is: $ y = 2x^2 + 3 $

$$ \text{Area} = \int_1^2 (2x^2 + 3) \, dx $$

Now, integrate the function:

$$ \text{Area} = \left[ \frac{2x^3}{3} + 3x \right]_1^2 $$

Substitute the limits $x = 2$ and $x = 1$:

$$ \text{Area} = \left( \frac{2(2)^3}{3} + 3(2) \right) - \left( \frac{2(1)^3}{3} + 3(1) \right) $$

$$ \text{Area} = \left( \frac{2(8)}{3} + 6 \right) - \left( \frac{2(1)}{3} + 3 \right) $$

$$ \text{Area} = \left( \frac{16}{3} + 6 \right) - \left( \frac{2}{3} + 3 \right) $$

$$ \text{Area} = \left( \frac{16}{3} + \frac{18}{3} \right) - \left( \frac{2}{3} + \frac{9}{3} \right) $$

$$ \text{Area} = \frac{34}{3} - \frac{11}{3} $$

$$ \text{Area} = \frac{23}{3} $$

Final Answer: The area under the curve is $ \frac{23}{3} $ square units.

How location beneath the Curve Calculator Works?

An online region under a curve calculator finds the region below curve with integration by way of following these pointers:

Input:

First of all, input a curve feature.
Now, substitute the higher and lower limit.
Then, pick the variable for integration from the drop-down list.
Hit the calculate button to compute the AUC.

Output:

The location beneath curve calculator gives the region and critical steps.
within the essential steps, the calculator integrates the curve feature term-by way of-time period for acquiring the effects.

FAQ:

Can the location be bad?

The place can't be negative. If the problem is to locate the value of the necessary, the result can be poor.

What does the place below the normal curve suggest?

The region below the regular distribution curve expresses chance and the entire AUC sum. maximum of the information values in a ordinary distribution have a tendency to merge, and further a cost from the suggest.