Help convert answer from Theta to x (TRIG SUB)

[windbreakerkid]

Please, help convert answer in terms of X and if you see anything wrong please let me know thank you

 

[BigBeachBanana]

I briefly looked at your work. Are you required to use trig-sub? The problem can be done with ordinary u-sub.
Let [imath]u=9x^2-1[/imath].

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Anyways, to find [imath]\tan(\theta)[/imath]:
[math]\sec(\theta)=\frac{1}{\cos(\theta)}=\frac{\text{Hypotenuse}}{\text{Adjacent}}=\frac{3x}{1}[/math]Then, the opposite side is [imath]\sqrt{(3x)^2-1^2}=\sqrt{9x^2-1}[/imath]
Then, [math]\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=\frac{\sqrt{9x^2-1}}{1}=\sqrt{9x^2-1}[/math]

 

[Deleted member 4993]

View attachment 31138
Please, help convert answer in terms of X and if you see anything wrong please let me know thank you

3x = sec(t)

tan^2(t) = 9x^2 - 1...... Edited

tan(t) = ?

Contiue....

 

[BigBeachBanana]

3x = sec(t)

tan^2(t) = 1 - 9x^2

tan(t) = ?

Contiue....

Did you mean [imath]-\tan^2(t) = 1 - 9x^2?[/imath]

 

[Deleted member 4993]

Did you mean [imath]-\tan^2(t) = 1 - 9x^2?[/imath]

yes .... and I edited my post above.

 

[lex]

Just to add, the problem can be done very easily by parts:
[math]\int_{ }^{} {x^2 \cdot \dfrac{x}{\sqrt{9x^2-1}}\,dx}[/math]

 

[Deleted member 4993]

Just to add, the problem can be done very easily by parts:
[math]\int_{ }^{} {x^2 \cdot \dfrac{x}{\sqrt{9x^2-1}}\,dx}[/math]

yes - but OP started with trig. substitution - so continuing with trig is advisable to reduce Khan-fusi on!!

By the way. I would have started with trig too! The form of the OP is too inviting!!

 

[lex]

@Subhotosh Khan
I agree! (It was only parenthetical).

 

[Steven G]

yes .... and I edited my post above.

And I can't delete my post if I desire to because......

 

[Steven G]

You have the wrong expression for dx
How did d(theta) suddenly appear out of nowhere? Is it by some magic?
You needed to square 3x: You know that 3x = sec(theta)--you wrote that somewhere on your page! So square both sides and get (3x)^2 = sec^2(theta). You instead said that 3x=9[((1/3)sec(theta))]^2 which while correct is a bit messy.
I would not let u = asec(theta) and u= tan(theta). If you want to use two substitutions that is perfectly fine. Just use different letters for the two u-subs--like u and v.

 

[Deleted member 4993]

And I can't delete my post if I desire to because......

The owner of the site does not trust you

 

[Steven G]

The owner of the site does not trust you

The sad part is that the owner trust you!

 

[Deleted member 4993]

The sad part is that the owner trust you!

I did not have to change my name!!

 

[Steven G]

I did not have to change my name!!

Neither did I