Area Under Curve Calculator solves the input function and gives the output in the blink of an eye. Enter input function and range in the fields of the input section and press on the calculate button to find the area under the given curve in the fraction of seconds.

**Area Under Curve Calculator: **Are you searching for a tool that solves the area under the given curve? Then you are at the right place. This handy calculator tool will help you to get the accurate answer along with the step by step process easily. Get to know the process on how to find the area under curve by hand in the following sections.

Area under the given function having lower and upper limits are given by the definite integration. Have a look at the below sections to get the clear step by step explanation to find the area under curve manually.

- Let us take any function f(x) and limits x = a, x = b
- Apply the definite integration to the function with limits upper as b and lower limit as a.
- Calculate the integration and substitute a and b values in the result.
- Subtract f(b) from f(a) to get the answer.

**Example**

**Question: Find the area of the region under the curve y = x ^{2} + 1 having x = 0 and x = 1?**

**Solution:**

Given that,

y = x^{2} + 1

Area = ∫_{0}^{1} x^{2} + 1 dx

= x^{3}/3 + x ]_{0}^{1}

= (1/3 + 1) - (0/3 + 0)

= 1+3 / 3

= 4/3

Area = 4/3

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**1. What is the formula to calculate the Area Under the Curve?**

The simple formula to get the area under the curve is as follows

A = ∫_{a}^{b} f(x) dx.

Where, a and b are the limits of the function

f(x) is the function.

**2. What is the definition of area under the curve?**

Area under the curve is the definite integral of a curve that describes the variation of a drug concentration in blood plasma as a function of time. It is a measure of how much drug reaches the person bloodstream in a period of time after a dose is given. This information is helpful in determining dosing and identifying potential drug interactions.

**3. Why does the antiderivative of a function give you the area under the curve?**

If you integrate the function f(x), then you will get the anti derivative of F(x). By evaluating the antiderivative over a specific domain [a, b] gives the area under the curve. Otherwise, perform F(b) - F(a) to find the area under f(x).

**4. Calculate the area under the curve of a function, f(x) = 7 – x ^{2}, the limit is given as x = -1 to 2?**

f(x) = 7 - x^{2} and limits x = -1 to 2

Area = ∫_{-1}^{2} (7 - x^{2}) dx

= 7x - x^{3}/3 ]_{-1}^{2}

= (7x2 - 2^{3} / 3) - (7(-1) - (-1)^{3}/3)

= [(42 – 8)/3] – [(1 – 21)/3]

= (34 + 20)/3

= 54/3

Area = 18