Dive into some fascinating examples of integrals, complete with detailed solutions!
Example 1: Basic Integral
Evaluate the integral: ∫ x^2 dx
Solution:
The antiderivative of x^2 is (1/3)x^3 + C, where C is the constant of integration.
Example 2: Definite Integral
Evaluate the integral from 0 to 1: ∫ (2x + 3) dx from 0 to 1
Solution:
First find the antiderivative: x^2 + 3x. Then, compute [1^2 + 3(1)] - [0^2 + 3(0)] = 4.