And what is that trick you did of closing the term..never seen that..I assume it's the same as replacing B with 1 minus A and solving which I think is more intuitive and clear right? Thanks for sharing
It is a fast way of finding the A, B values. It is similar to multiplying both sides of the equality with the denominator of A and then setting the value of the variable as the value which was making the denominator of A zero.
@@ArifSolvesIt I don't see how that is relevant..finding where the denominator is zeronis not relevant or useful in helping you find the values of A or B right so I don't see why you do it? Or why anyone would think of it.
I don't see why or how anyone would ever think ofnthst substitution so why use that at all?? Why not do integration by parts or some other substitution like t equals b*cosine theta or something else? Thanks for sharing though.
This substitution is very crucial and it is used to solve certain types of integrals that you may not solve by using other methods. In solving integrals, of course, there are multitude of different ways to do it. However, the method I showed here helps us simplify certain types of integrals (like the one I solved here; especially when you have the combination of sine and cosine functions of the integration variable in the denominator of the integrand) significantly.
@@ArifSolvesIt but here you only have cosine so don't you agree no one would.ever think of it if you hadn't seen it beforehand and therefore why not solve this another wah??
And why would you draw such a. Complicated right triangle..that's not needed right just make one triangle.with angle theta over 2 and the opposite side is t and the adjacent side is 1 so tangent theta equals t/1 which is same as t...why not just do that??
you can do that, but it does not help you find sin(theta) and/or cos(theta). Hence, t=tan(theta/2); i.e. t is given as the tangent of the HALF of the angle. But, we need to find sine and cosine of the FULL angle. So, if you want to find sin(theta) or cos(theta), drawing just one triangle does not help.
@@ArifSolvesIt but don't you agree NO ONE would.EVER.think of making that substitution of.tan half theta unless you knew ahead of time that was the answer.so should he considered unfair and why nkt use another substitutionlike cosine or sine or something .thanks for answering.
![Integrating using t=tan(x/2) substitution - [The Weierstrass substitution]](http://i.ytimg.com/vi/QCAtgZRelno/mqdefault.jpg)
Fantastic
And what is that trick you did of closing the term..never seen that..I assume it's the same as replacing B with 1 minus A and solving which I think is more intuitive and clear right? Thanks for sharing
It is a fast way of finding the A, B values. It is similar to multiplying both sides of the equality with the denominator of A and then setting the value of the variable as the value which was making the denominator of A zero.
@@ArifSolvesIt I don't see how that is relevant..finding where the denominator is zeronis not relevant or useful in helping you find the values of A or B right so I don't see why you do it? Or why anyone would think of it.
I don't see why or how anyone would ever think ofnthst substitution so why use that at all?? Why not do integration by parts or some other substitution like t equals b*cosine theta or something else? Thanks for sharing though.
This substitution is very crucial and it is used to solve certain types of integrals that you may not solve by using other methods. In solving integrals, of course, there are multitude of different ways to do it. However, the method I showed here helps us simplify certain types of integrals (like the one I solved here; especially when you have the combination of sine and cosine functions of the integration variable in the denominator of the integrand) significantly.
@@ArifSolvesIt but here you only have cosine so don't you agree no one would.ever think of it if you hadn't seen it beforehand and therefore why not solve this another wah??
And why would you draw such a. Complicated right triangle..that's not needed right just make one triangle.with angle theta over 2 and the opposite side is t and the adjacent side is 1 so tangent theta equals t/1 which is same as t...why not just do that??
you can do that, but it does not help you find sin(theta) and/or cos(theta). Hence, t=tan(theta/2); i.e. t is given as the tangent of the HALF of the angle. But, we need to find sine and cosine of the FULL angle. So, if you want to find sin(theta) or cos(theta), drawing just one triangle does not help.
@@ArifSolvesIt but don't you agree NO ONE would.EVER.think of making that substitution of.tan half theta unless you knew ahead of time that was the answer.so should he considered unfair and why nkt use another substitutionlike cosine or sine or something
.thanks for answering.
@@ArifSolvesIt but you don't need sine of the full.angle you only.need cosine for.this integral..