Study Group Reminder - Review who.
Rapid Recall
- Which problems are you ready to present?
- Which problems did you sincerely attempt
- Find the area of a parallelogram whose edges are the vectors $(-1,3)$ and $(4,2)$.
- Fill in the missing pieces in the following equation: $$\int_{-1}^{2}e^{5x}dx = \int_{?}^{?}e^{u}(?)du.$$
- Draw the region whose area is given by the double integral $$\int_{-2}^{1}\int_{x}^{2-x^2}dydx.$$
Group problems
- Find the area of a triangle with vertices $(1,0)$, $(0,2)$, and $(5,5)$.
- Draw the region in the plane described by $-1\leq x\leq 2$ and $x\leq y\leq 4-x^2$.
- Compute the integral $\ds\int_{x}^{4-x^2}dy$ (assume $x$ is a constant).
- Compute the double integral $\ds \int_{-1}^{2}\left(\int_{x}^{4-x^2}dy\right)dx$.
- Draw the region in the $xy$ plane described by $\pi/2\leq \theta \leq \pi$ and $0\leq r\leq 5$.
- Compute the integral $\ds\int_{0}^{5}rdr$.
- Compute the double integral $\ds \int_{\pi/2}^{\pi}\left(\int_{0}^{5}rdr\right)d\theta$.
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