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What does the Fundamental Theorem of Calculus, Part 1 state?
If $g(x) = \int_{a}^{x} f(t) dt$, then $g'(x) = f(x)$.
What does the Fundamental Theorem of Calculus, Part 2 state?
If $F(x)$ is an antiderivative of $f(x)$, then $\int_{a}^{b} f(x) dx = F(b) - F(a)$.
Define definite integral.
An integral with upper and lower limits, resulting in a numerical value.
What is an antiderivative?
A function whose derivative is the original function.
Define the Fundamental Theorem of Calculus.
A theorem that connects the derivative and the integral, stating that differentiation and integration are inverse processes.
What is the formula for FTOC Part 1?
$g(x) = \int_{a}^{x} f(t) dt \implies g'(x) = f(x)$
What is the formula for FTOC Part 2?
$\int_{a}^{b} f(x) dx = F(b) - F(a)$, where F is the antiderivative of f.