Definite Integral of Tan x
We know that, by the fundamentals properties of definite integrals, we can calculate the definite integral of tan x within any two time intervals limits.
Definite Integral of f(x) = [Tex]\int_a^b f(x)\ dx~=~F(b) – F(a)[/Tex]
Definite Integral of f(x) within ‘a’ to ‘b’ interval = [Tex]\int_a^b tan\ x\ dx~=~|ln\ sec \ x|_a^b~=~|ln\ sec \ b|~-~|ln\ sec \ a| [/Tex]
Using the above property to calculate the definite integral of tan x. Let’s take an example of definite integral of tan x between the time interval π/4 and π/3.
we know that, [Tex]\int tan x dx = ln |sec x| + C[/Tex]
Then ,[Tex]\int_{\pi/4}^{\pi/3} tan\ x\ dx = ln|sec \ \pi/3| – ln|sec\\pi /4|[/Tex]
we know that,
- sec π/ 3 = 2
- sec π/ 4 = √(2)
so, [Tex]\int_{\pi /4}^{\pi / 3} tan\ x\ dx~=~ln |2| – ln|\sqrt{2|}[/Tex]
we know that, ln|a| – ln|b| = ln|a/b|
so, [Tex]\int_{\pi /4}^{\pi /3} tan\ x\ dx~=~ln |2/\sqrt{2}|~=~0.3465735902799727[/Tex]
Integral of Tan x
Integral of tan x is ln |sec x| + C. Integral of tan x refers to finding the integration of the trigonometric function tan x with respect to x which can be mathematically formulated as ∫tan x dx. The tangent function, tan x, is an integrable trigonometric function that is defined as the ratio of the sine and cosine functions.
This article discusses the formula for the integral of tan x along with derivation, definite integral of tan x, and integral of tan inverse x. We will also discuss some solved examples based on the integral of tan x along with Practice Questions and FAQs.
Table of Content
- What is Integral of Tan x?
- Integral of Tan x Formula
- How to do Integration of tan x dx?
- Definite Integral of Tan x
- Integration of Tan Inverse x
Contact Us