Check your answers after you've solved this equation.

$$t^2=9 t$$

Use polar coordinates to evaluate

$$\int_{0}^{1} \int_{0}^{\sqrt{1-x^{2}}} \cos \left(x^{2}+y^{2}\right) d y \ d x$$

Convert from rectangular to polar coordinates: (a) (1, 0) (b)

$$( 3 , \sqrt { 3 } )$$

(c) (-2, 2) (d)

$$( - 1 , \sqrt { 3 } )$$

Check your answers after you've solved this equation.

$$y^2-3 y+2=0$$

Find an equation in x and y that has the same graph as the polar equation. Use it to help sketch the graph in an r$\theta$-plane.

r cos $\theta$=5

Find an equation in $x$ and $y$ that has the same graph as the polar equation. Use it to help sketch the graph in an $r \theta$-plane.

$$r^2 \sin 2 \theta=4$$

Sketch the region

$$\mathcal { D }$$

indicated and integrate f(x, y) over

$$\mathcal { D }$$

using polar coordinates.

$$f ( x , y ) = e ^ { x ^ { 2 } + y ^ { 2 } } ; \quad x ^ { 2 } + y ^ { 2 } \leq R$$

Find an equation in $x$ and $y$ that has the same graph as the polar equation. Use it to help sketch the graph in an $r \theta$-plane.

$$r^2 \cos 2 \theta=1$$

Find an equation in x and y that has the same graph as the polar equation. Use it to help sketch the graph in an r$\theta$-plane.

r=-5

Find an equation in $x$ and $y$ that has the same graph as the polar equation. Use it to help sketch the graph in an $r \theta$-plane.

$$r=2$$

Graph the set of points whose polar coordinates satisfy the given equations and inequalities.
$\theta=\pi / 2, \quad r \leq 0$

Sketch the region

$$\mathcal { D }$$

indicated and integrate f(x, y) over

$$\mathcal { D }$$

using polar coordinates.

$$f ( x , y ) = \sqrt { x ^ { 2 } + y ^ { 2 } } , \quad x ^ { 2 } + y ^ { 2 } \leq 2$$

Use polar coordinates to determine the area bounded on the right by the unit circle $x^{2}+y^{2}=1$ and bounded on the left by the vertical line $x=\sqrt{2} / 2$.

Given problem refer to the plane region R bounded by the curve $y=x-x^2$ and the x-axis.

Find the coordinates of the centroid of R.