How do you use induction here? You haven't even given us a result!anirudhsharma1 said:pi
∫sin^2(nx)/sin^2(x) dx
0
I tried using mathematical induction and did arrive at the correct result but was wondering if a better method could be used to solve it?
Are you confused about what induction means?anirudhsharma1 said:putting n=1,n=2
we get pi, and pi as the result
so i generalised it for 'n'.
thats the reason i asked for the solution because this is definitely an improper method.
Definite integration is a mathematical process used to find the area under a curve between two points on the x-axis. It is represented by the symbol ∫ and involves finding the antiderivative of a given function.
The multiple angle formula for sine is sin(nx) = n(sin x)cos^n-1 (x) - C. This formula is used to simplify expressions involving multiple angles of sine.
To integrate multiple angles of sine, you can use the multiple angle formula for sine or other trigonometric identities to simplify the expression. Then, you can use the standard integration techniques such as substitution, integration by parts, or trigonometric substitution.
Definite integration involving multiple angles of sine is important in various fields of science and engineering, such as physics, astronomy, and electrical engineering. It is used to solve problems involving periodic functions and to calculate areas, volumes, and other quantities in real-life applications.
Some tips for solving definite integration involving multiple angles of sine include using trigonometric identities to simplify the expression, choosing the appropriate integration technique, and paying attention to the limits of integration. It is also helpful to practice and familiarize yourself with common integration patterns.