SteamKing said:With you u substitution, all you have done is replace 'x' with 'u'. You haven't done any essential simplification to the integrand.
I would suggest looking at integration by parts. If you can find candidates for u and v with parts, then further substitution might be warranted.
The purpose of evaluating an integral is to find the exact numerical value of the area under a curve or the volume of a solid bounded by a surface. It is an important tool in calculus and is used in many fields of science and engineering to solve real-world problems.
To evaluate an integral, you need to use integration techniques such as substitution, integration by parts, or partial fractions. These techniques involve breaking down the integral into smaller, simpler parts and then using the fundamental theorem of calculus to find the solution.
A definite integral has specific limits of integration, while an indefinite integral does not. This means that the value of a definite integral represents a specific area or volume, while an indefinite integral represents an entire family of functions that differ only by a constant.
Evaluating integrals is commonly used in physics to calculate work, force, and displacement. It is also used in economics to analyze supply and demand curves, in statistics for probability distributions, and in engineering to model and design structures and systems.
Yes, there are some limitations to evaluating integrals. Some integrals cannot be solved using traditional techniques and require advanced methods such as numerical integration. Additionally, not all functions have an antiderivative, which means they cannot be evaluated using integration.