The Attempt at a Solution
t=√x ; x=t^2 ; dx= 2t
The last part of an integral is the result, also known as the definite integral, which represents the area under a curve between two points on a graph. It is typically denoted by the symbol ∫ and is often used in calculus and other branches of mathematics.
To calculate the last part of an integral, one must first determine the upper and lower limits of integration, which represent the two points on the graph between which the area is being calculated. Then, the function being integrated must be evaluated at these limits and the difference between the two values is taken as the result.
The last part of an integral is important because it allows us to find the exact area under a curve, which has numerous applications in mathematics, physics, and other fields. It also allows us to solve differential equations and evaluate complex functions that cannot be easily solved using other methods.
There are several techniques for evaluating the last part of an integral, including substitution, integration by parts, and using trigonometric identities. These techniques can be used to simplify the integral and make it easier to calculate the result.
Yes, there are some limitations to using the last part of an integral. For example, it can only be used for continuous functions and may not always give an exact result for more complex functions. It also requires a good understanding of calculus and mathematical concepts to accurately evaluate the integral.