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Area Between Curve and X Axis Calculator Online

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The Area Between Curve and X Axis Calculator helps users calculate the area enclosed by a curve and the x-axis over a specified interval. This is useful in various fields such as physics, engineering, and economics, where understanding the area under a curve can provide insights into accumulated quantities, total output, and other important measures.

Formula

To calculate the area between a curve and the x-axis, follow these steps:

  1. Identify the function f(x) and the interval [a, b] over which you want to find the area.
  2. Set up the definite integral. The formula for the area A is: A = ∫ from a to b of |f(x)| dx
  3. Evaluate the integral to find the area.
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Pre-calculated Areas Table

Below is a table with pre-calculated areas for common functions over typical intervals:

Function f(x)Interval [a, b]Area A
x^2[0, 1]1/3
sin(x)[0, pi]2
e^x[0, 1]e - 1

This table provides a quick reference for common calculations, saving time and effort.

Example Calculation

Let's calculate the area between the curve f(x) = x^2 and the x-axis over the interval [0, 1]:

  1. Identify the function f(x) = x^2 and the interval [0, 1].
  2. Set up the definite integral: A = ∫ from 0 to 1 of x^2 dx
  3. Evaluate the integral: A = [x^3 / 3] from 0 to 1 = 1/3 - 0/3 = 1/3

Thus, the area between the curve f(x) = x^2 and the x-axis over the interval [0, 1] is 1/3.

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Most Common FAQs

What is the area under a curve?

The area under a curve refers to the space between the curve and the x-axis over a specified interval. It can be calculated using definite integrals.

Why is the absolute value used in the integral?

The absolute value ensures that the area is always positive, regardless of whether the curve is above or below the x-axis.

How can this calculator be useful in real life?

This calculator can be used in various real-life scenarios, such as calculating the total distance traveled by an object.

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