Question 5 i) Consider the double integral I = integral 1 = ₁²₁₁ e²² dx dy. y/3 Draw the region of integration then compute I. It will be necessary to reverse the order of integration to perform the computation. ii) A property o(x, y) = ky acts on a region D = {(x, y) = R² | x² + y² ≤ a², y ≥ 0}. Compute the cumulative effect of a on D, Q=ffo(x, y) da a) using cartesian coordinates, and b) using cylindrical coordinates.
Question 5 i) Consider the double integral I = integral 1 = ₁²₁₁ e²² dx dy. y/3 Draw the region of integration then compute I. It will be necessary to reverse the order of integration to perform the computation. ii) A property o(x, y) = ky acts on a region D = {(x, y) = R² | x² + y² ≤ a², y ≥ 0}. Compute the cumulative effect of a on D, Q=ffo(x, y) da a) using cartesian coordinates, and b) using cylindrical coordinates.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 5
i) Consider the double integral I =
हरुर
dx dy.
y/3
Draw the region of integration then compute I. It will be necessary to reverse
the order of integration to perform the computation.
ii) A property o(x, y) = ky acts on a region D = {(x, y) = R² | x² + y² ≤a², y ≥ 0}.
Compute the cumulative effect of o on D,
2=11₂0 o(x, y) da
a) using cartesian coordinates, and
b) using cylindrical coordinates.
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