Because it's quite a bit simpler to integrate t sin(at) than to integrate (6 - 3t)sin(at). In both cases you need to use integration by parts, but the simpler integrand makes the process easier.Ry122 said:Could someone please explain to me why this is split into two separate terms?
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A simple integral is a mathematical concept that represents the area under a curve in a graph. It is denoted by the symbol ∫ and is used to find the total value of a function over a given interval.
To solve a simple integral, you need to follow these steps:
Some common integration rules include the Power Rule, which states that the integral of x^n is (x^(n+1))/(n+1), and the Constant Multiple Rule, which states that the integral of kf(x) is k times the integral of f(x). Other rules include the Sum Rule, Product Rule, and Chain Rule.
Yes, many scientific and graphing calculators have built-in integration functions that can be used to solve simple integrals. However, it is important to understand the concept and steps of integration to ensure accurate results.
Simple integrals have many real-life applications, such as calculating the area under a curve to determine the volume of a container or the amount of paint needed to cover a wall. They are also used in physics to calculate work, in economics to find the total profit or loss, and in biology to model population growth.