Step 1: Identify the function to integrate, which is (2x + 1).
Step 2: Find the antiderivative of the function. The antiderivative of 2x is x^2, and the antiderivative of 1 is x. So, the antiderivative of (2x + 1) is x^2 + x.
Step 3: Write the definite integral using the antiderivative. We need to evaluate [x^2 + x] from 1 to 3.
Step 4: Substitute the upper limit (3) into the antiderivative: (3^2 + 3) = (9 + 3) = 12.
Step 5: Substitute the lower limit (1) into the antiderivative: (1^2 + 1) = (1 + 1) = 2.
Step 6: Subtract the result of the lower limit from the result of the upper limit: 12 - 2 = 10.
Definite Integral – The process of calculating the area under a curve defined by a function over a specific interval.
Fundamental Theorem of Calculus – Relates differentiation and integration, allowing the evaluation of definite integrals using antiderivatives.
