Evaluating Definite Integrals: Step-by-Step Example using Math Notation

(integral a-. b) equals

The notation “(integral a-b)” usually represents the definite integral of a function over a given interval

The notation “(integral a-b)” usually represents the definite integral of a function over a given interval. The notation indicates that we are integrating the function over the interval from “a” to “b”.

To evaluate the definite integral, we need to follow these steps:

Step 1: Find the antiderivative of the function.
Step 2: Evaluate the antiderivative at the upper limit (b), and subtract the value obtained from evaluating the antiderivative at the lower limit (a).

Let’s consider an example to demonstrate this process. Suppose we want to evaluate the definite integral from 1 to 4 of the function f(x) = x^2.

Step 1: Find the antiderivative of the function.
To find the antiderivative of x^2, we can use the power rule. Applying the power rule, we add 1 to the exponent and divide by the new exponent:
∫ x^2 dx = (1/3)x^3 + C

Step 2: Evaluate the antiderivative at the upper limit (b) and subtract the value obtained from evaluating the antiderivative at the lower limit (a).
∫(1-4) x^2 dx = [(1/3)x^3] evaluated from 1 to 4
= [(1/3)(4)^3] – [(1/3)(1)^3]
= (64/3) – (1/3)
= 63/3
= 21

Therefore, the value of the definite integral from 1 to 4 of the function f(x) = x^2 is equal to 21.

Please note that this is just an example to demonstrate the process of evaluating definite integrals. Different functions may require different techniques to find their antiderivatives.

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