Catherine R.

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.