How to Find the Area Over an Interval Using Integrals.





Introduction: How to Find the Area Over an Interval Using Integrals.

In this instuctable, you will be able to learn how to find the area under the curve using integrals.

Step 1: Materials

  • Paper
  • Pencil
  • Calculator
  • Equation
  • Interval

Step 2: Know the Standard Form for Integrals.

The standard form for integrals is in the picture provided.

Step 3: Come Up With an Equation.

For example, lets use the equation 9x^2-4x+2. plug this into your f(x).

Step 4: Now Figure Out Over What Interval You Want to Find the Area Of.

So lets say you want to find the area between 1 and 5. Plug the value 1 in as your "a" and the value 5 as your "b"

Step 5: Find the Integral of Your Equation.

For every 'x' in the equation, you will add n+1 to the exponent. After doing so, you will divide the coefficient (the number in front of that variable) by the new exponent. If there is a number without a variable, remember that it has a variable of x^0.

Example: 9x^2 would now be (9/3)x^3

Step 6: Find the Area Over the Interval

With the new equation, you can now find the area over the interval. Take your value "b" and plug it into every variable 'x' of the equation. Do the same exact thing for your value "a." After, subtract your answer from the value "b" by your answer from "a" to get the area.

Example: f(b) - f(a)

Step 7: Now You Have the Area Over the Interval Using Integration!



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    11 Discussions

    Great! Thanks for sharing!

    Great, can you do it with an Arduino?

    Done too many of these in my life lol, great tutorial

    Nice job! I haven't looked at simple integration in a long time! This technique can also find the volume if the shape spins around the x-axis...this branch of calculus was always my favorite!

    This solution only works for taking integral a of polynomial equations it is not comprehensive

    thanks for teaching me integrals dude

    Most days I count myself fortunate to remember the correct order of operations . thank you.

    I think it's useful because it makes it clear what corresponds to a linear integral, but you can not understand how you get it nor even what is the differential. Like that, it's like believing to show the world the art of painting only showing just showed the process for a polynomial function, but things change when the function is exponential, rational, logarithmic ......


    2 years ago

    I think you mean to say, add 1 to the exponent, not n + 1.

    1 reply

    You are correct and it would work either way. When I learned it, I was told n+1 substituting the current exponent in for n to get your new exponent.

    Great clear description of how this is done! Thanks for sharing!