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"Wir müssen wissen, wir werden wissen!" -Hilbert

Catherine took her Master's of Science in Mathematics from Missouri State University. She is an Associate Professor in the Math Department at Mira Costa College & San Diego City College. Her research interests lie in Knot Theory and Differential Geometry. Teaching mathematics is the highlight of her day, and she firmly believes that every person has the ability to be a mathematician if they tap into their creative mind.

Catherine has a diversity of interests, including studying languages, sketching, ice skating, vocal performance, and enjoying the great outdoors. She is always up for an adventure!

Sketch the region enclosed by the given curves and find its area.

$ y = x^4 $ , $ y = 2 - \mid x \mid $

The rates at which rain fell, in inches per hour, in two different locations $ t $ hours after the start of a storm are given by $ f(t) = 0.73t^3 - 2t^2 + t + 0.6 $ and $ g(t) = 0.17t^2 - 0.5t + 1.1 $. Compute the area between the graphs for $ 0 \le t \le 2 $ and interpret your result in this context.

Find the area of the region bounded by the parabola $ y = x^2 $, the tangent line to this parabola at $ (1, 1) $, and the x-axis.

Find the number $ b $ such that the line $ y = b $ divides the region bounded by the curves $ y = x^2 $ and $ y = 4 $ into two regions with equal area.

(a) Find the number a such that the line $ x = a $ bisects the area under the curve $ y = \frac{1}{x^2} $, $ 1 \le x \le 4 $.

Find the values of $ c $ such that the area of the region bounded by the parabolas $ y = x^2 - c^2 $ and $ y = c^2 - x^2 $ is 576.