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Unformatted text preview: c is given by the integral 9. Find the polar equation for the graph of the Cartesian equation . Replacing x and y with r cos θ and r sin θ, respectively, gives
Equivalently,
.
10. A plate has the shape of a right triangle. One leg of the triangle is 12 cm and the other is 7 cm. When the
plate is placed with one vertex at the origin, one at the point (12, 0), and one at (12, 7), the mass density (in
grams per cm2) at any point (x, y) depends only on x and is given by δ(x) = x + 2. Find the mass of the plate.
This one is nearly copied from an old exam. Here is a sketch. y x Along that (red) vertical strip, the density is approximately constant. The mass of that strip is, then,
approximately equal to the product of its area and its density. In symbols,
.
So the total mass of the plate is equal to the integral...
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 Fall '1
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 Calculus

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