When you want to find the area under a curve, you can use different types of Riemann sums: left, right, or midpoint. Which one you choose often depends on what the function looks like. Let’s break it down:
Left Riemann Sums:
These work best when the function is going down.
For example, if you have a function like ( f(x) = -x^2 + 4 ), using the left points will give you a better guess of the area. That's because the left values are higher on a downward slope.
Right Riemann Sums:
These are great when the function is going up.
Take the function ( f(x) = x^2 ) for example. When you use the right points here, you get a more accurate estimate since the points add up to larger values.
Midpoint Riemann Sums:
These are usually the most accurate for any type of function.
They work by taking an average height over each section. This is especially useful for functions that wiggle around, like ( f(x) = \sin(x) ). Midpoint sums give a balanced estimate of the area.
To sum it up, pick the type of Riemann sum based on whether your function is increasing or decreasing!
When you want to find the area under a curve, you can use different types of Riemann sums: left, right, or midpoint. Which one you choose often depends on what the function looks like. Let’s break it down:
Left Riemann Sums:
These work best when the function is going down.
For example, if you have a function like ( f(x) = -x^2 + 4 ), using the left points will give you a better guess of the area. That's because the left values are higher on a downward slope.
Right Riemann Sums:
These are great when the function is going up.
Take the function ( f(x) = x^2 ) for example. When you use the right points here, you get a more accurate estimate since the points add up to larger values.
Midpoint Riemann Sums:
These are usually the most accurate for any type of function.
They work by taking an average height over each section. This is especially useful for functions that wiggle around, like ( f(x) = \sin(x) ). Midpoint sums give a balanced estimate of the area.
To sum it up, pick the type of Riemann sum based on whether your function is increasing or decreasing!