To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)
Top

Area under the Curve Calculator
Top
Area under a curve in general is the area coming under the curve. It can be calculated with respect to coordinates as the area above the axis minus area below the axis.

If function f(x) is given, then area under the curve between the given limits x = a and x = b is given as:

Area under curve = $\int_{a}^{b}$ f(x) dx.
Area under curve calculator (known as area under a curve calculator even as area under graph calculator) is a online tool to get the area under the curve hence called as area under curve calculator online that finds area under curve. You just have to enter the value of function, lower limit and upper limit and get the answer instantly.
You can see a default function with its lower and upper limit given below. When you click on "Calculate Area", the area under the curve is calculated by integrating the function between the two points.
 

Steps for Area under the Curve Calculator

Back to Top
Step 1 :  

Read the problem and observe the given curve function and the limits.



Step 2 :  

Use the formula:
Area of the curve = $\int_{a}^{b}$ f(x) dx.
Substitute the given function and the limits and integrate the function to get the answer.



Problems on Area under the Curve Calculator

Back to Top
  1. Find the area under the curve y = 5 - x2 and x-axis where x = -3 and x = 3.


    Step 1 :  

    given: The function is y = 5 - x2


    Limits are a = -3 and b = 3.



    Step 2 :  

    Area under the curve = $\int_{a}^{b}$ f(x) dx.
     
    Substituting the values of limits in f(x)

    $\int_{-3}^{3} (5 - x^{2})$ dx.
    = (5x - $\frac{x^{3}}{3})_{-3}^{3}$
    = (5(3) - $\frac{3^{3}}{3}$) - (5(-3) - $\frac{(-3)^{3}}{3}$)
    = (15 - 9) - (-15 + 9).
    = 15 - 9 + 15 -9
    = 12.



    Answer  :  

    $\therefore$ The area under the curve y = 5 - x2 = 12 units.



  2. Find the area under the curve y = sin x where the point lies between a = $\pi$ and b = 2 $\pi$.


    Step 1 :  

    given: The given function is f(x) = y = sin x


    The limits are a = $\pi$ and b = 2 $\pi$. 



    Step 2 :  

    Area under the curve = $\int_{a}^{b}$ f(x) dx where a and b are lower limits.


    Substituting the values of limits in f(x)

    $\int_{\pi}^{2 \pi}$ sin x dx.
    = - $(cos x)_{\pi}^{2 \pi}$
    = -[cos $2\pi$ - cos $\pi$]
    = -[1 - (-1)]
    = -2



    Answer  :  

    The area under the curve y = sin x is -2 units.



*AP and SAT are registered trademarks of the College Board.