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11 C h 5 Apical Date: Name: The Definite Integral (5.2) Recall: we were interested in computing the following limit of an infinite sum: n LIM f (xi *)x n i 1 Definition: If f is a continuous function
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How to fill out definite integral:

01
Determine the function: Start by identifying the function that you want to integrate. This could be a mathematical equation or a real-world scenario that can be modeled mathematically.
02
Define the limits of integration: Determine the lower and upper limits of integration, denoted as "a" and "b" respectively. These limits specify the range over which you want to calculate the area or accumulated value.
03
Express the integral: Write down the expression for the definite integral using the integral symbol (∫), the function, and the limits of integration. It should look something like this: ∫ f(x) dx from a to b.
04
Evaluate the integral: Proceed to solve the integral expression. This may involve applying integration techniques, such as substitution, integration by parts, or recognizing special formulas. Work through the steps carefully to obtain the result.
05
Calculate the definite integral: Plug in the values of the limits of integration into the integrated function and simplify the expression. This will give you the specific value that represents the area under the curve or the accumulated total.

Who needs definite integral?

01
Mathematics Students: Definite integrals are commonly taught and studied in mathematics courses, particularly in calculus. Students learning about integration techniques, applications of integration, or advanced mathematical topics will encounter definite integrals.
02
Engineers and Scientists: Many professionals in fields such as engineering, physics, chemistry, and economics rely on definite integrals to solve real-world problems. These problems often involve determining areas, volumes, rates of change, and accumulated values.
03
Financial Analysts: Definite integrals can be used in finance to calculate the present value of future cash flows, perform risk analysis, or evaluate investment opportunities. Financial analysts utilize these techniques to make informed decisions and assess the performance of financial instruments.
04
Economists: In economics, definite integrals are employed to calculate consumer and producer surplus, which measure the benefits and costs associated with economic transactions. Economists also use integrals to analyze production functions and study economic growth.
Overall, anyone seeking to understand and analyze quantities that change continuously over a given interval would benefit from knowing how to fill out definite integrals.

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