Integrals with fractional powers of trig (1 Viewer)

[mrpotatoed]

how would you do the indefinite integral of

(sinx)^5/2 * cosx

so basically the integral of sinx to the power of 5/2 multiplied by cosx. Sorry I don't know how to use that fancy maths thingy that people on here seem to use on here yet. Thanks in advance.

 

[Ekman]

Its just reverse chain rule, however you could also use the substitution u=sinx, and solve it accordingly

 

[mrpotatoed]

Thanks man, just another one, how would you do the indefinite integral of (cosx)^2 / (sinx)^4

Is there a way apart from T-formula?

 

[Ekman]

Thanks man, just another one, how would you do the indefinite integral of (cosx)^2 / (sinx)^4

Is there a way apart from T-formula?

You can let u=cotx or just use reverse chain rule again since:

 

[mrpotatoed]

oh god im retarded how did I not see that

 

[mrpotatoed]

Another unrelated question.. thought I may as well do it here instead of adding another thread

Consider the curve y=(x^5)-10(x^4)+22(x^3)+32(x^2)-20x+20. Find the equation of the line which intersects the curve at (-2,-180) and is a tangent to the curve at two other points.

 

[Drsoccerball]

Another unrelated question.. thought I may as well do it here instead of adding another thread

If k>27/4, prove that (x^3)-kx+k=0 has three real roots

and

Consider the curve y=(x^5)-10(x^4)+22(x^3)+32(x^2)-20x+20. Find the equation of the line which intersects the curve at (-2,-180) and is a tangent to the curve at two other points.

For the first question ill get you started :









Ill look at the second one gimme a sec

 

[Drsoccerball]

Consider the curve y=(x^5)-10(x^4)+22(x^3)+32(x^2)-20x+20. Find the equation of the line which intersects the curve at (-2,-180) and is a tangent to the curve at two other points .

This isn't possible do you mean at one other point?

 

[mrpotatoed]

This isn't possible do you mean at one other point?

Nup, two others points...as a matter of fact, when I tried to do this question I got an unreal solution as one of the x values for the tangent so I was also thinking it is impossible, but someone else has done it. (They won't show me how though )

FYI I got the first question so that can be ignored

 

[Drsoccerball]

Nup, two others points...as a matter of fact, when I tried to do this question I got an unreal solution as one of the x values for the tangent so I was also thinking it is impossible, but someone else has done it. (They won't show me how though )

FYI I got the first question so that can be ignored

Using my way ? or some other way
And i sketched the graph theres no way you can possibly have an intersection and two other tangents one i understand from the sketch of it but two i dont know..

 

[FrankXie]

Another unrelated question.. thought I may as well do it here instead of adding another thread

Consider the curve y=(x^5)-10(x^4)+22(x^3)+32(x^2)-20x+20. Find the equation of the line which intersects the curve at (-2,-180) and is a tangent to the curve at two other points.

hint, this is equivalent to that the quintic equation has one root x=-2 and two double roots, where y=ax+b is the mentioned tangent.

 

[FrankXie]

hint, this is equivalent to that the quintic equation has one root x=-2 and two double roots, where y=ax+b is the mentioned tangent.

and from here, i got the double roots are , and the tangent is

 

[mrpotatoed]

Thanks guys, I went back and found I did another arithmetic error of 10+2=8 giving me unreal roots lol... and I got the same as you frankxie

 

[mrpotatoed]

Sorry... got another integrals question but don't want to create a new thread...

If we have an equation such as (x^2-1)/(x^2-5x+6), the answers do +(-5x+7)-(-5x+7), so that you have two integrals, the first cancels out to 1, and the second has a degree of 1 while the denominator has a degree of 2. They use partial fractions, but I used an addition / subtraction method the same as what you would have to do if the denominator is irrational. However I end up with a different answer. I was just curious if this is because this method does not work when the denominator can be factorised, or if the constant is just different or something.