Thank you for making this video and also whenever you put colors in it. It becomes more beautiful and let's me feel as if calc 2 is easy although it's not.
Only if you don’t change back into terms of the original variable. If you are referring to example 2 in the video, notice that after I integrate in terms of u I substitute back what u was set equal to (2y). By doing that there is no need to change the bounds of integration. However, you could also leave the integral in terms of u, but then you would have to update the bounds by plugging in the values into what you set u equal to. In other words, there’s two different ways to go about it, I chose to go back into terms of y but you could do it differently, you’ll get the same answer regardless. Hope this helps!
The disk and washer methods are very similar. In fact, they involve the same formula/process. The disk method is just an easier case of the washer method when the inner radius is 0. So in other words, if you have only an outer radius function, you use the disk method, but if you have both an inner radius and outer radius represented by functions that are not just 0, then you use the washer method.
Thank you for making this video and also whenever you put colors in it. It becomes more beautiful and let's me feel as if calc 2 is easy although it's not.
Thanks again my guy!
Thanks you sooooo much ❤
You're welcome!
For the last exercise, case b where y =-2, for the small radius, you have r(x) = 0-(-2), Should that be r(x) =5 -(-2) instead?
I made a mistake. Please ignore my comment above.
Perfect
i might be remembering wrong/mistaken but when you do U sub dont you need to update the bounds of the integral?
Only if you don’t change back into terms of the original variable. If you are referring to example 2 in the video, notice that after I integrate in terms of u I substitute back what u was set equal to (2y). By doing that there is no need to change the bounds of integration. However, you could also leave the integral in terms of u, but then you would have to update the bounds by plugging in the values into what you set u equal to. In other words, there’s two different ways to go about it, I chose to go back into terms of y but you could do it differently, you’ll get the same answer regardless. Hope this helps!
when do i use disk and washer
The disk and washer methods are very similar. In fact, they involve the same formula/process. The disk method is just an easier case of the washer method when the inner radius is 0. So in other words, if you have only an outer radius function, you use the disk method, but if you have both an inner radius and outer radius represented by functions that are not just 0, then you use the washer method.
@@JKMath I see thank you for the explanation !!
@@ritvikindupuri2388 No problem! 👍
❤❤❤❤