I always get confused at functions that are ambigously show themselves as two different ones but are two of the same type. Like in q3 here. I thought this would need integration by parts for -2x^3= algebraic and e^-x^4 = exp. Thats what im looking for in ur videos like which one to take as multiple func and which one not
My advice would be to always check for u-sub before moving onto a more complicated solution like parts. With practice, you should be able to recognize when you have something like x^2sin(x^3), we see u-sub works because the function inside the sine has a derivative equal to a multiple of the other function. Or, x^(-2)e^(x^-1), same idea. For Q3 in the video, If you were to try parts and set v = e^-x^4 you'd quickly arrive at an impasse, since we cannot integrate that into elementary functions. If you set u = e^-x^4, you'd probably realize you should be using u sub once you found du/dx = -x^3e^-x^4. Always stay on the lookout for u-sub! Another kind that's easy to miss is something like sin(sqrt(x)) / sqrt(x).
No idea - perhaps you're misreading the homework problem? The solution in the video is correct. If you're not misreading the problem, then the answer key must have a typo.
That works fine - but to me it always seems like a waste of time to do it that way. I don't know if I talk about why I do it the way I do in this video. If not, maybe I do in this one: th-cam.com/video/qhnHDr1g4sY/w-d-xo.html Not a big deal either way though - whichever way makes more sense to you, they're both the same at the core!
I always get confused at functions that are ambigously show themselves as two different ones but are two of the same type. Like in q3 here. I thought this would need integration by parts for -2x^3= algebraic and e^-x^4 = exp. Thats what im looking for in ur videos like which one to take as multiple func and which one not
My advice would be to always check for u-sub before moving onto a more complicated solution like parts. With practice, you should be able to recognize when you have something like x^2sin(x^3), we see u-sub works because the function inside the sine has a derivative equal to a multiple of the other function. Or, x^(-2)e^(x^-1), same idea.
For Q3 in the video, If you were to try parts and set v = e^-x^4 you'd quickly arrive at an impasse, since we cannot integrate that into elementary functions. If you set u = e^-x^4, you'd probably realize you should be using u sub once you found du/dx = -x^3e^-x^4.
Always stay on the lookout for u-sub! Another kind that's easy to miss is something like sin(sqrt(x)) / sqrt(x).
What should I do when I get (-x dx) after substitution and in question I got x^3 dx
Can you tell whats the sequence in which these functions should be done is it ilate or liate
I'm not sure what you mean, what is ilate and liate?
@@WrathofMath its an abreviation of inverse. Log. Algeraic. Trig. Exp
at 7:00, I have this exact problem on my homework and it's showing this answer as incorrect. Not really sure what else to do!
No idea - perhaps you're misreading the homework problem? The solution in the video is correct. If you're not misreading the problem, then the answer key must have a typo.
@@WrathofMath no, you are wrong.
No I’m not, but I’d be happy to tell you where you are wrong if you can tell me where you think I am wrong
Sir, how do we solve this?
Use a proof by contradiction to show that if 𝑛2 − 1 is odd, then 𝑛 is even.
I always make the dx the whole subject of du with nothing on the dx side in this case tried to do -1/4x^3 du = dx and got the same answer
That works fine - but to me it always seems like a waste of time to do it that way. I don't know if I talk about why I do it the way I do in this video. If not, maybe I do in this one: th-cam.com/video/qhnHDr1g4sY/w-d-xo.html
Not a big deal either way though - whichever way makes more sense to you, they're both the same at the core!
why did you just make this more confusing