Category: Integrals (Page 4 of 5)

The first quiz problem is a definite integral. We started by thinking about what the function \(f(x) = \sqrt[4]{x}\) looks like when graphed, with the bounds \(x=1\) and \(x=16\). This region is not a “nice” geometric shape — so computing the area will require the Fundamental Theorem of Calculus.

Today’s quiz focused on the interpretation of our notation: \(\displaystyle\int_a^b f(x)\, dx\). This notation refers to the area between \(f(x)\) and the \(x\)-axis, from \(x=a\) to \(x=b\).

Today’s quiz covered the Riemann Sum. The given function was \(f(x) = x^2 – 9\), and you were asked to identify where the function intersected the \(x\)-axis. These two intersections were then used as the start and end of our interval for approximating the area bounded by \(f(x)\).