20190523

• I-Learn, Problem Set, Class Pictures

If you are a little witty over a period of time, what do you get?

Rapid Recall

1. Find the area of a parallelogram whose edges are parallel to the vectors $(\cos\theta dr,\sin\theta dr)$ and $(-r\sin\theta d\theta,r\cos\theta d\theta)$.
2. When we add up lots of little bits of area, so $\int_R dA$, what do we get?
3. Draw the region described by $\pi/6\leq \theta\leq \pi/3$ and $4\leq r\leq 5$.

Group problems

1. Consider the polar curve $r=7$. Compute $\frac{dx}{d\theta}$ and $\frac{dy}{d\theta}$. Then use the arc length formula $$\int_C\sqrt{\left(\frac{dx}{d\theta}\right)^2+\left(\frac{dy}{d\theta}\right)^2}d\theta$$ to find the arc length for the portion of this curve with $0\leq \theta\leq \alpha$.
2. Draw the region in the $xy$ plane described by $0\leq \theta \leq \pi$ and $0\leq r\leq 2\sin3\theta$.
3. Draw the region in the $xy$ plane described by $0\leq \theta \leq \pi$ and $0\leq r\leq 3\sin2\theta$.
4. Set up a double integral that gives the area of the region in the $xy$ plane that lies inside one petal of the rose $r=3\cos2\theta$.
5. Draw and shade the region in the $xy$ plane that lies inside the curve $r=3+2\cos\theta$ and outside the curve $r=1$.
6. Set up a double integral that gives the area of the region in the $xy$ plane that lies inside the curve $r=3+2\cos\theta$ and outside the curve $r=1$.

Problem Set
Today

• Sep24, Oct, Nov, Dec