Riemann integral

Imagine you have a big piece of cake and you want to know how much frosting is on it. One way you could do that is by cutting the cake into small pieces and adding up the amount of frosting on each piece. This is kind of like what a Riemann integral does.

In math terms, the Riemann integral is a way to calculate the area under a curve. This curve could represent anything, like the distance a car travels in time or the temperature of a room over time.

To calculate the Riemann integral, you first divide the area under the curve into small, equal rectangles. How many rectangles you make depends on how accurate you want your answer to be - the more rectangles you use, the more precise your answer will be.

Then, you calculate the area of each rectangle (which is just the width times the height). Finally, you add up the areas of all the rectangles to get an estimate of the total area under the curve.

This estimate gets more and more accurate as you make the rectangles smaller and smaller (imagine cutting the cake into teeny, tiny pieces). Eventually, you can get a really good estimate of the true area under the curve.

And that's the Riemann integral in a nutshell! It's a way to estimate the area under a curve by dividing it into small rectangles and adding up their areas.