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 down the definite integral from 1 to 3: [x^2 + x] from 1 to 3.
Step 4: Evaluate the antiderivative at the upper limit (3): (3^2 + 3) = (9 + 3) = 12.
Step 5: Evaluate the antiderivative at the lower limit (1): (1^2 + 1) = (1 + 1) = 2.
Step 6: Subtract the lower limit result from the upper limit result: 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.
