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education/math/MATH1210 (calc 1)/Integrals.md

@@ -53,6 +53,10 @@ $$ \int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i = 1}^n f(x_i)\Delta x$$
 
 $f(x_i)$ is the *height* of each sub-interval, and $\Delta x$ is the change in the *x* interval, so $f(x_i) \Delta x$ is solving for the area of each sub-interval.
 
+- If your function is always positive, then the value of a definite integral is the area under the curve.
+- If the function is always negative, then the value of a definite integral is the area above the curve to zero.
+- If the function has both positive and negative values, the output is equal to the area above the curve minus the area below the curve.
+
 ## Examples
 > Find the exact value of the integral $\int_0^1 5x \space dx$