Math Problem Statement
definite integral from 0 to pi/7 of sec(x)tan(x)
Solution
The integral you are asking for is:
We know that the derivative of is . Therefore, we can directly integrate as follows:
Now, we apply the limits from 0 to :
Since , the result simplifies to:
This is the exact value of the definite integral:
Would you like further details on how this was solved or explanations on secant and tangent functions? Here are some related questions:
- What is the geometric interpretation of the secant and tangent functions?
- How can we apply substitution methods to similar integrals?
- What are common derivatives involving secant and tangent?
- How would the integral change if the limits were different?
- What are some applications of integrals involving trigonometric functions?
Tip: When dealing with integrals of trigonometric functions, recognizing derivatives of standard functions can simplify the problem greatly.
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Math Problem Analysis
Mathematical Concepts
Calculus
Definite Integral
Trigonometric Functions
Formulas
Integral of sec(x)tan(x) dx = sec(x) + C
Fundamental Theorem of Calculus
Theorems
Fundamental Theorem of Calculus
Suitable Grade Level
Grades 11-12
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