1. The problem statement, all variables and given/known data
Integrate:[tex]I=\int_{-π/4}^{π/4} \ln{(\sec θ-\tan θ)}\,dθ[/tex]
2. Relevant equations
Properties of definite integrals, basic integration formulae, trigonometric identities.
3. The attempt at a solution
By properties of definite integrals, the same integral I wrote as equivalent to[tex]I=\int_{-π/4}^{π/4} \ln{(\sec θ+\tan θ)}\,dθ[/tex].
Because[tex]\int_{a}^{b} f(x)\,dx=\int_{a}^{b} f(a+b-x)\,dx[/tex](replacing θ by π/4-π/4-θ) Now, I think of adding these two integrals to form an equation and solving for [itex]I[/itex] but I'm messing up. Am I doing wrong? Is there any better/easy way?
Thanks for your time and help.
Integrate:[tex]I=\int_{-π/4}^{π/4} \ln{(\sec θ-\tan θ)}\,dθ[/tex]
2. Relevant equations
Properties of definite integrals, basic integration formulae, trigonometric identities.
3. The attempt at a solution
By properties of definite integrals, the same integral I wrote as equivalent to[tex]I=\int_{-π/4}^{π/4} \ln{(\sec θ+\tan θ)}\,dθ[/tex].
Because[tex]\int_{a}^{b} f(x)\,dx=\int_{a}^{b} f(a+b-x)\,dx[/tex](replacing θ by π/4-π/4-θ) Now, I think of adding these two integrals to form an equation and solving for [itex]I[/itex] but I'm messing up. Am I doing wrong? Is there any better/easy way?
Thanks for your time and help.
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