Each iterated integral represents the volume of a solid. Make a sketch of the solid. (You do not have to find the volume.) ∫ − 2 2 ∫ − 2 2 x 2 + y 2 d x d y
Each iterated integral represents the volume of a solid. Make a sketch of the solid. (You do not have to find the volume.) ∫ − 2 2 ∫ − 2 2 x 2 + y 2 d x d y
Each iterated integral represents the volume of a solid. Make a sketch of the solid. (You do not have to find the volume.)
∫
−
2
2
∫
−
2
2
x
2
+
y
2
d
x
d
y
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Consider the solid whose base is the region bounded by the x-axis, y = x, and y=-4x + 5. Find the volume of the solid if the slices perpendicular to the
y-axis are rectangles with height sin(y).
Give the exact volume below in the form A + B sin(C) where A, B and C are constants to be determined.
Click on the symbol for the equation editor to enter in math mode.
b
a
sin (a)
∞
a
A pontoon is to be made in the shape shown. The pontoon is designed by rotating the graph of y = 1 − (x2/16), −4 ≤ x ≤ 4 about the x-axis, where x and y are measured in feet. Find the volume of the pontoon.
Determine the area and the centroid (x (bar), y (bar)) of the area.
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