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Easy: Linear and quadratic functions
The Fundamental Theorem of Calculus: ∫ from a to b of f(x) dx = F(b) − F(a), where F is any antiderivative of f. Find F (no + C is needed), substitute the upper limit, substitute the lower limit, and subtract in that order. The average value of f on [a, b] is that integral divided by b − a.
Evaluate.
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No. The constant appears in F(b) and F(a) and cancels when you subtract.
Only when the function stays above the x-axis. Parts below the axis count as negative, so the integral is a net (signed) area.
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