haruspex said:Have you looked at what happens if you substitute y = 1/x in the integral and the use the equation to substitute for f(1/y)?
justwild said:well If I do that I shall be returning to the same problem statement...
The bounds of integration are determined by the given condition, which typically involves a relationship between the independent variable and the function being integrated. This condition can be used to set up an equation or inequality that will help determine the lower and upper limits of integration.
Some common conditions include a specific value for the dependent or independent variable, a relationship between the limits of integration, or a known relationship between the function and its derivative.
The method used to evaluate a definite integral with a given condition will depend on the specific condition and the function being integrated. Some common methods include substitution, integration by parts, and trigonometric substitution.
Yes, a definite integral with a given condition can have multiple solutions, especially when the condition provides a range of values for the integral. In these cases, it is important to carefully analyze the given condition to determine the appropriate bounds of integration.
To check your solution, you can use the fundamental theorem of calculus, which states that the definite integral of a function is equal to the difference of its antiderivative evaluated at the upper and lower limits of integration. You can also use a graphing calculator or computer program to verify your solution.