Questions from General Calculus

Q: A region R is shown. Decide whether to use polar coordinates

A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and write ∬R f (x, y) dA as an iterated integral, where f is an arbitrary continuous function o...

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

Evaluate the given integral by changing to polar coordinates. ∬R y^2/(x^2 + y^2 ) dA, where R is the region that lies between the circles x2 + y2 = a2 and x2 + y2 = b2 with 0 < a < b

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

Evaluate the given integral by changing to polar coordinates. ∬D e^(-x^2-y^2 ) dA, where D is the region bounded by the semicircle x = √(4 - y^2 ) and the y-axis.

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

Evaluate the given integral by changing to polar coordinates. ∬R cos √(x^2 + y^2 ) dA, where D is the disk with center the origin and radius 2

Q: Find ∫_0^2 f (x,y) dx

Find ∫_0^2 f (x,y) dx and ∫_0^3 f(x,y) dy f (x, y) = x + 3x2y2

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

Evaluate the given integral by changing to polar coordinates. ∬D x dA, where D is the region in the first quadrant that lies between the circles x2 + y2 = 4 and x2 + y2 = 2x

Q: Calculate the iterated integral ∫_1^4 ∫_0^

Calculate the iterated integral ∫_1^4 ∫_0^2 (6x^2 y - 2x) dy dx

Q: Find the maximum and minimum volumes of a rectangular box whose surface

Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose total edge length is 200 cm.

Q: Calculate the iterated integral ∫_0^1 ∫_0^

Calculate the iterated integral ∫_0^1 ∫_0^1 (x+y)^2 dx dy

Q: Evaluate the double integral. ∬D x cos y dA

Evaluate the double integral. ∬D x cos y dA, D is bounded by y = 0, y = x2, x = 1