Im glad I found this channel. It made me realize that font can play a big role in absorbing the information. The rounded strokes make calculus feel less intimidating.
I got a bit uneasy on the last example b/c you left the lower and upper limits as the x values 0 and 8 when you expressed the integral in terms of u. I thought you were going to plug those in, but then you changed it all back in terms of x and it was worked out. I tell students to write x=0 and x=8 if they choose to go back to the x world. I find it a bit easier to to use u=1 and u=5 to evaluate the integral. No harm no foul though, but it does lead to confusion when x and u appear in the same integral.
Thanks for the feedback! My go-to strategy is to always go back in terms of x, so that is the method I chose to show. However I do agree that writing the limits as x=0 and x=8 is the better approach. And although I do show that step in my video on u-sub for calc 1, I did leave it out in this video which was not focused on u-sub. I never want to confuse anyone, so I will be sure to make that step more clear in future recordings. Thanks again!
Which example are you referring to? Or are you talking about the arc length formula? If you are talking about the formula, the square root and square cannot be canceled out because not everything under the square root is being squared. You have 1 + (f'(x))² under the square root, not (1 + (f'(x))²)². You can't take the square root of 1 and (f'(x))² individually. Both terms as a whole, as one quantity, would need to squared in order to algebraically cancel out the square and square root.
I just really wanted to say thank you this is the best math channel on youtube!
Im glad I found this channel. It made me realize that font can play a big role in absorbing the information. The rounded strokes make calculus feel less intimidating.
講解得好清楚
讚 !
holy shit, this is a way shorter explaination for the formula than the professor leonard's one. thanks
I got a bit uneasy on the last example b/c you left the lower and upper limits as the x values 0 and 8 when you expressed the integral in terms of u. I thought you were going to plug those in, but then you changed it all back in terms of x and it was worked out. I tell students to write x=0 and x=8 if they choose to go back to the x world. I find it a bit easier to to use u=1 and u=5 to evaluate the integral. No harm no foul though, but it does lead to confusion when x and u appear in the same integral.
Thanks for the feedback! My go-to strategy is to always go back in terms of x, so that is the method I chose to show. However I do agree that writing the limits as x=0 and x=8 is the better approach. And although I do show that step in my video on u-sub for calc 1, I did leave it out in this video which was not focused on u-sub. I never want to confuse anyone, so I will be sure to make that step more clear in future recordings. Thanks again!
No he was right at last he substituted u with what it was but also using u as 1 and 5 is also true
Why dont square root and square just cancel, and you just deal with multiplying it out
Which example are you referring to? Or are you talking about the arc length formula? If you are talking about the formula, the square root and square cannot be canceled out because not everything under the square root is being squared. You have 1 + (f'(x))² under the square root, not (1 + (f'(x))²)². You can't take the square root of 1 and (f'(x))² individually. Both terms as a whole, as one quantity, would need to squared in order to algebraically cancel out the square and square root.
@@JKMathoh okay i understand, i did mean the formula
@@JKMathearned a sub thank you