Question 5 (Area Integrals) Consider the parallelogram bounded from the bottom by y = 0 and from the top by y = H, from the left by the line y = ax and from the right by the line y = a (x - L), where a, L, H > 0. 1. Sketch this shape 2. Write the area of the parallelogram as a double integral, where the integral in is evaluated first. 3. Evaluate this integral

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 5 (Area Integrals)
Consider the parallelogram bounded from the bottom by
0 and from the top by y = H, from the left by the
ax and from the right by the line
=
y = a (x − L), where a, L, H > 0.
-
1. Sketch this shape
y
line y =
-
2. Write the area of the parallelogram as a double
integral, where the integral in is evaluated first.
3. Evaluate this integral
4. Find the expressions for the two vectors V₁, V2 that
describe the bottom and left side of the parallelogram,
respectively.
5. Verify that the area found in question 3 is v₁ × V₂|.
Transcribed Image Text:Question 5 (Area Integrals) Consider the parallelogram bounded from the bottom by 0 and from the top by y = H, from the left by the ax and from the right by the line = y = a (x − L), where a, L, H > 0. - 1. Sketch this shape y line y = - 2. Write the area of the parallelogram as a double integral, where the integral in is evaluated first. 3. Evaluate this integral 4. Find the expressions for the two vectors V₁, V2 that describe the bottom and left side of the parallelogram, respectively. 5. Verify that the area found in question 3 is v₁ × V₂|.
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