Hi everyone! Today I am going to show you how to derive and find the formula of the volume of square pyramids using integration in calculus.
The formula for the volume of any shape is the definite integral from one end of the shape (let's call it "a") to the other end of the shape (let's call this "b"). So the integral is from a to b of the area of the cross-section (If you cut or slice the shape, you find the area of the open surface) and then dx. We are trying to find the volume of square pyramids.
Here, the area of the cross-section of the square pyramid is a square! You guessed it! The area of a square is the base to the power of two, or the base squared. Since we are integrating with respect to y, make sure to rewrite the base in terms of y. I show you how to do it in my video. After you find the area of the cross-section, you can substitute it with the area in the definite integral volume formula.
In the next video, I will show you a few practice problems on finding the volume of unique shapes.
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