Simple Indefinite Integral

What is the indefinite integral of $y = 100x^2$

To solve the indefinite integral of the function where y equals one hundred times x squared, we are essentially looking for the antiderivative. An indefinite integral finds the original function from its derivative, but since we don't know the specific starting point, the solution includes a constant of integration. The goal of an indefinite integral is to reverse the process of differentiation.

For this specific problem, we can solve it by using a basic rule of integration: the power rule. The power rule is used when the variable is raised to a power, and it allows us to "undo" the derivative by increasing the exponent and adjusting the coefficient. In this case, you’ll increase the exponent by one and divide by the new exponent, while keeping the constant multiplier one hundred in place.

Indefinite integrals are key in calculus because they help us understand the accumulation of quantities and reverse differentiation. As you progress through the course, you’ll encounter more complex functions that require advanced techniques, like substitution, which changes variables to simplify the integral, or integration by parts, which breaks down more complicated products of functions. These methods will help solve harder problems where simple rules like the power rule won’t be enough.

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