- #1
Jeremy
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My class, teacher included, cannot seem to figure out the integral of the square root of tan x. Maybe someone here can help?
thanks,
jeremy
thanks,
jeremy
As helpful as usual...dextercioby said:It's much more interesting to consider
[itex] \int \sqrt{\sin x} \ dx [/itex]
Daniel.
What's interesting about the integral:dextercioby said:It's much more interesting to consider
[itex] \int \sqrt{\sin x} \ dx [/itex]
Daniel.
arildo said:[tex]\int\frac{2u^{2}du}{\sqrt{1-u^{4}}}[/tex]
dx said:while were on the topic of integrating expressions that contain square roots of trigonometric functions, I was having a hard time a while ago evaluating this
[tex]\int{\frac{1}{\sqrt{sin x}}dx[/tex]
Not really. Oh, I forgot, I'm not in CalcI.Orion1 said:
Any Calculus I students interested in integrating this equation?
[tex]\int \frac{dx}{\sqrt{\tan x}}[/tex]
Orion1 said:
Data, why is that 'not an equation', please elaborate and clarify your statement.
Orion1 said:
I understand, I posted a short-hand integrand expression and called it an equation.
Then what are your equations for this specific integrand expression?
"Data Denominator Theorem" ?! Did you invent that? It makes no sense to me at all.Orion1 said:
I understand, a CalcI student should use the Data Denominator Theorem.
Data Denominator Theorem:
[tex]\int \frac{1}{u(x)}} dx = F(x) + C[/tex]
Of course he did.TD said:"Data Denominator Theorem" ?! Did you invent that? It makes no sense to me at all.
Jeremy said:My class, teacher included, cannot seem to figure out the integral of the square root of tan x. Maybe someone here can help?
thanks,
jeremy
The integral of the square root of tangent x is equal to 2/3 * tan^(3/2) x + C
, where C is a constant of integration.
To solve an integral with a square root of tangent x, you can use the substitution method. Let u = tan x
and du = sec^2 x dx
. Then the integral becomes ∫√(tan x) dx = ∫√u * du = 2/3 * u^(3/2) + C = 2/3 * tan^(3/2) x + C
.
No, the integral of the square root of tangent x cannot be evaluated using basic integration rules. It requires the use of substitution or other advanced integration techniques.
Yes, the integral of the square root of tangent x is only defined for values of x where tan x > 0
. This means that x must be in the interval (-π/2, π/2)
or any interval that is 2π
units away from it.
Yes, the integral of the square root of tangent x can be expressed in terms of elementary functions. It can be written as 2/3 * tan^(3/2) x + C
, which is a combination of trigonometric and power functions.