Examples on Integral of Sec x
Various examples on Integral of Sec x
Example 1. Evaluate ∫sec(x).dx
Solution:
sec(x) = 1/cos(x)
Substitute u = sin(x), so du = cos(x)dx.
Now, (∫cos(x). dx = ∫1/u.du)
= ∫1/u.du
= ln |u| + c
= ln |sin (x)| + c
Example 2. Determine ∫sec(x).tan(x).dx
Solution:
Let,
- u = sec(x)
- du = sec(x) tan(x) dx
Thus,
= ∫sec(x) tan(x), dx
= ∫du
= u + C
= sec(x) + C
Example 3. Find ∫sec2(x).dx.
Solution:
= ∫sec2(x).dx
Using Power Rule for Integration
= tan(x) + C
So, ∫sec2(x), dx = tan(x) + C, where C is Constant of Integration
Example 4. Calculate ∫sec(x)/tan(x).dx.
Solution:
Let,
- u = tan(x)
- du = sec2(x).dx
Substituting (u) and (du), we get:
= ∫ 1/u.du
= ln|u| + C
Substituting, u = tan(x)
= ln| tan(x)| + C
Integral of Sec x
Integral of sec x is ∫(sec x).dx = ln| sec x + tan x| + C. Integration of the secant function, denoted as ∫(sec x).dx and is given by: ∫(sec x).dx = ln| sec(x) + tan(x)| + C. Sec x is one of the fundamental functions of trigonometry and is the reciprocal function of Cos x. Learn how to integrate sec x in this article.
In this article, we will understand the formula of the integral of sec x, Graph of Integral of sec x, and Methods of Integral of sec x.
Table of Content
- What is Integral of Sec x?
- Integral of Sec x Formula
- Integral of Sec x by Substitution Method
- Integral of Sec x by Partial Method
- Integral of Sec x by Trigonometric Formula
- Integral of Sec x by Hyperbolic Functions
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