Interactive Area Under a Curve
The problem seems simple, but is difficult.
The solution seems difficult, but is simple.
Why Is Finding the Area Under a Curve Difficult
We know how to find the area of basic shapes such as rectangles, squares, triangles, and circles.
We have an area formula for each basic shape, but we don't have an area formula for curves.
We can easily calculate the areas of basic shapes because we can define them, they have rules, a square has 4 points and 4
equal sides, a rectangle has 4 points and 2 sets of equal sides, and a circle is all the points a certain distance from a center point.
Now if you scribble a curve on a piece of paper, what are the rules of the shape you drew? They are unknow, so how could we find the area when we know nothing about it.
How to Find the Area Under a Curve
We know how to find the area of a rectangle;
let's turn our curve into a group of rectangles;
we could then find the area of each rectangle and then add them together.
Simple, it is just multiplication and addition.
We must have the function of the curve (if we can graph it then we have the function). The function tells us the height of one of our rectangles, we control how the width of our rectangles. The skinnier our rectangles are the more we will need, but the more accurate our area will be.
If we have a function for a curve we can calculate it's area easily with code.
Convert Problems We Can't Solve
We always try to convert problems we're stuck on into problems we know how to solve.
Sometimes, this will require more steps, but it will bring us to the solution.
Remember, if we get stuck, we should try to convert the problem.
Conclusion
At the core of integral calculus is a simple idea that helps us to solve all types of problems. We ought not to be intimidated by calculus, rather we should view it as a versatile, powerful tool that we can take advantage of.