what is the difference between using shell method and the disc method to calculate volume. Is one better than the other?
They each have their draw backs in levelof difficulty depending upon the problem
how do u know which one to use?
remember what is important is how the figure sits relative to your axis of rotation...so draw the picture and identify the axis of rotation when you are rotating your figure around the axis can you take slices perpendicular to the axis and these slices will be disks....make sure there are no problems with subtracting one function from the other where R is outside function and r is inside function.....that is disk...okay? now shell okay?
so do you use shell when you are rotating it around a line that isn't horizontal or vertical?
Shell is taking your slices parallel to the axis of rotation and these little slices , when you rotate them around the axis of rotation , form shells or sort of like little cans one inside the other. So we are going to sum these circular cans or shells .
You can do either but with a vertical axis of rotation it is often easier to use shell since the slices are perpendicular to x-axis which means you integrate dx not dy
oh...so if it is difficult to change a y= equation into x= when revolving it around the y-axis...it is easier to use shell because you can use the y= equation as the height and x as the shell radius...is that right?
exactly! The functions you are working with will help you decide which method to use. Let the axis of rotation and what will be your dy or your dx be your guide.
okay...thanks for all your help! i haven't taken math in years and I've been trying to explain the disc and shell method to one of my friends but clearly i didn't remember it as well as i thought i did.
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