Integral Calculus
Integral Calculus
star_batch_jee_advanced_2025
Grade None
Question:
The value of the integral $\int_0^\pi \frac{\sin(n+1/2)x}{\sin x/2} dx$ $(n \in \mathbb{N})$ is:
Step-by-Step Solution
Key Concept: Dividing by a high power of $x$ converts a difficult rational integral into a form that may be recognized or more easily substituted.
Divide both numerator and denominator by $x^{10}$ to get $\int \frac{5x^{-5} + 4x^{-6}}{(1 + x^{-4} + x^{-5})^2}dx$. This integral is standard and can be solved through recognition or substitution techniques applicable to reciprocal polynomial forms.
Correct Answer: 4