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
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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