Questions from General Calculus

Q: Evaluate the given integral by changing to polar coordinates. ∬

Evaluate the given integral by changing to polar coordinates. ∬R arctan (y/x) dA, where R = {(x, y) | 1 < x2 + y2 < 4, 0 < y < x}

Q: Express D as a region of type I and also as a

Express D as a region of type I and also as a region of type II. Then evaluate the double integral in two ways. ∬x y dA, D is enclosed by the curves y = x2, y = 3x

Q: A long piece of galvanized sheet metal with width w is to

A long piece of galvanized sheet metal with width w is to be bent into a symmetric form with three straight sides to make a rain gutter. A cross-section is shown in the figure. (a). Determine the di...

Q: Let V be the volume of the solid that lies under the

Let V be the volume of the solid that lies under the graph of f (x, y) = √(52 - x^2 - y^2 ) and above the rectangle given by 2 < x < 4, 2 < y < 6. Use the lines x = 3 and y = 4 to divide R into sub r...

Q: Draw an example of a region that is (a).

Draw an example of a region that is (a). both type I and type II (b). neither type I nor type II

Q: Suppose X and Y are random variables with joint density Function f

Suppose X and Y are random variables with joint density Function f (x, y) = {_0^0.1 e-(0.5x+0.2y) if x > 0, y > 0 otherwise. (a). Verify that f is indeed a joint density function. (b). Find the follow...

Q: Suppose that X and Y are independent random variables, where X

Suppose that X and Y are independent random variables, where X is normally distributed with mean 45 and standard deviation 0.5 and Y is normally distributed with mean 20 and standard deviation 0.1. (a...

Q: Describe in words the surface whose equation is given. r

Describe in words the surface whose equation is given. r = 2

Q: Write the equations in cylindrical coordinates. (a). 2x2

Write the equations in cylindrical coordinates. (a). 2x2 + 2y2 - z2 = 4 (b). 2x - y + z = 1

Q: A cylindrical shell is 20 cm long, with inner radius 6

A cylindrical shell is 20 cm long, with inner radius 6 cm and outer radius 7 cm. Write inequalities that describe the shell in an appropriate coordinate system. Explain how you have positioned the coo...