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Understanding Indefinite Integrals
Indefinite integrals, also known as antiderivatives, are a fundamental concept in calculus. They represent the family of all functions whose derivative is the given function.
More formally, if F'(x) = f(x), then the indefinite integral of f(x) is:
∫f(x) dx = F(x) + C
where C is the constant of integration.
Here's a quick example:
Given f(x) = 3x2, find the indefinite integral.
∫3x2 dx = x3 + C
This is because the derivative of x3 is 3x2.