jd12345 said:Homework Statement
Find the value of ∫ ( sin 37x / sin x )dx - from 0 to π
Homework Equations
The Attempt at a Solution
Well i tried doing it by parts but it makes its more complicated. I tried to expand sin 37x as sin(36+1)x but could not solve it. I am lost
A definite integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value of a function between two specific points on the x-axis.
The definite integral is calculated by dividing the area under the curve into smaller rectangles and adding up the areas of all the rectangles. This is known as the Riemann sum. As the number of rectangles increases, the approximation of the definite integral becomes more accurate.
A definite integral has specific limits of integration, whereas an indefinite integral does not. This means that a definite integral will give a numerical value, while an indefinite integral will give a function with a constant of integration.
The definite integral has many applications in real life, such as calculating the area under a velocity-time graph to find the total distance traveled, or finding the total amount of water in a tank by integrating the flow rate over time. It is also used in physics, engineering, and economics, among other fields.
The fundamental theorem of calculus states that the definite integral of a function is equal to the anti-derivative of that function evaluated at the two limits of integration. In other words, the definite integral and the derivative are inverse operations of each other.