In this video, I showed how to use varieous integration technique to integrate a rational radical integrand
Пікірлер: 36
@killer_queen23146 ай бұрын
It's been a while since I've watched one of your videos also sorry I failed your class😅
@lawrencejelsma81186 ай бұрын
If among all other memory requirements you have to know the integrals of sec(x) and sec^3(x) in a test ... Where does memorizing trig integrals end? 😬 ... then I guess I fail his class too. 😢 Lucky for me I'm not in integral Calculus and have a long list of Integral cheat sheet trig formulas of CRC tables to avoid that problem on my job!! 😂
@Sg190th6 ай бұрын
What if you used hyperbolic sub?
@naturallyinterested75696 ай бұрын
Then you'd find the -ln|...| in the solution be replaced with -1/2 * arccosh(2x+3)
@hazwi6 ай бұрын
at the end, you can get rid of the absolute value on the natural log since the sum of square roots is always positive
@DEYGAMEDU6 ай бұрын
Sir I have sent you a derivative question in your mail, please solve that
@The_Bad_AntАй бұрын
Awesome explain, thank you teacher 💐💙 31/8/2024 SATURDAY 10:52 AM
@dougaugustine40753 ай бұрын
Double substitution and a pair of trig identities. Wow.
@Mephisto7076 ай бұрын
The absolute value inside ln in the final answer is unnecessary.
@FOUADNAJATMAАй бұрын
❤
@hosseinmortazavi790325 күн бұрын
Nice professor
@canyoupoop6 ай бұрын
2:55 Do you "SEE" a problem in both of those indefinite integrals?
@icannotchoose6 ай бұрын
This is very well explained! I'd love to see more integral problems like this.
@atrixiousscramasax66864 ай бұрын
whats sec
@leonmancaj36906 ай бұрын
Bless you good man
@Mehrdad_Basiry-fj4rl6 ай бұрын
Fantastic question...🎉🎉🎉. Learn new methods...
@SodiqjonSobirov-w5h5 ай бұрын
Thank you teacher
@zeravam6 ай бұрын
I used the sustitution sen^2(theta)=1/(x+2), obtaining: cosec(theta)=sqr(x+2) and cotan(theta)=sqr(x+1). My integral was: (2cosec(theta)-2cosec^3(theta)) I had a equivalent result: ln|sqr(x+2)-sqr(x+1)|+sqr((x+2)(x+1))
@fantasypvp6 ай бұрын
The first thing i thought wheb i saw that integral was to immediately put x+1 = tan^2(u), then the top simplifies, the bottom turns to sec and simplifies, so youve got the integral of sin(u) * dx/du du
@flamewings32246 ай бұрын
To be honest, I don’t know why am I continuing to learning integration math more… I think I’ve found it funny and interesting since my hight school. So, for last question in the video, we actually can get rid of absolute value inside the natural logarithm, cause inside we have a sum of two square roots, which is always greater than zero, so we don’t need absolute value. But… Is it a mistake to just leave it here?
@BhaiyaMathsWaale6 ай бұрын
Use x+1=t^2 Very easy question
@jaychirmade6 ай бұрын
Can we use the standard formula for √(x^2-a^2)?
@marcgriselhubert39156 ай бұрын
When you arrive at sqrt(u^2 - 1) better use u = cosh(t), with t >0
@trinugroho38326 ай бұрын
sir, can you explain how can u^2-1 be sec theta?
@surendrakverma5556 ай бұрын
Thanks Sir for excellent explanation and good handwriting. 😊
@enejedhddhd68826 ай бұрын
I already memorized radical x^2 - a^2 formula😂 i had an ode exam yesterday
@joeykraftx94446 ай бұрын
Nice. if we let ch t=u as 2nd substitution i find the resolution much easier.
@holyshit9226 ай бұрын
(x+1)/(x+2) = u^2 This substitution lead us to integrating rational function without any secants After substitution proposed by me integration by parts will simplify partial fraction decomposition
@PrimeNewtons6 ай бұрын
Yes, that works too. Answer looking slightly different.
@JourneyThroughMath6 ай бұрын
As far as the plus/minus is concerned, couldnt you ha e factored it out as a constant and then your final answer is +_answer?
@JourneyThroughMath6 ай бұрын
If Im not much mistaken you can drop the absolute value. Both square roots are greater than 0.
@Tisakoreann6 ай бұрын
AMAZING
@m.h.64706 ай бұрын
Wolfram Alpha gives a very different result. Looks like your result only works for x > -1, so only for the real numbers. If you want complex solution, your way doesn't work.
@niloneto16086 ай бұрын
Because the function itself is only defined for x>-2. And usually complexo numbers doesn't associate with integrals of a single variable function.
@Tomorrow326 ай бұрын
@@niloneto1608Yes, my friend. When you see a problem, think of never dividing by zero. X can approach -2 but never reaches it. X is real by definition.
@m.h.64706 ай бұрын
The function is undefined at x = -2 and is 0 at x = -1, but x < -2 and -2 < x < -1 can be calculated. The results for x < -2 are complex numbers, but they are still possible. And according to Wolfram Alpha, the integral CAN be calculated, so that these values are included.