Step 1: Identify the function to integrate, which is (2x + 3).
Step 2: Find the antiderivative of the function. The antiderivative of 2x is x^2, and the antiderivative of 3 is 3x. So, the antiderivative of (2x + 3) is x^2 + 3x.
Step 3: Write the definite integral using the antiderivative. We need to evaluate [x^2 + 3x] from 1 to 2.
Step 4: Substitute the upper limit (2) into the antiderivative: (2^2 + 3*2) = (4 + 6) = 10.
Step 5: Substitute the lower limit (1) into the antiderivative: (1^2 + 3*1) = (1 + 3) = 4.
Step 6: Subtract the result of the lower limit from the result of the upper limit: 10 - 4 = 6.
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.
