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Suppose that c is the line segment from (a, b) to (c,d). (a) Show that [rd |x dy – y dx = ad – bc Briefly describe what this integral represents geometrically. Hint: Think back to linear algebra. What do determinants measure? (b) Suppose that a polygon P has vertices {(₁, Y₁)}_₁ in counter-clockwise order. Use Green's theorem to show that P has area: 1 A = [(x1Y2 −X2Y1) + (X2Y3 − X3Y2) + ... + (Xn-1Yn — XnYn−1) + (XnY1 − X1Yn)]

Suppose that c is the line segment from (a, b) to (c,d). (a) Show that [rd |x dy – y dx = ad – bc Briefly describe what this integral represents geometrically. Hint: Think back to linear algebra. What do determinants measure? (b) Suppose that a polygon P has vertices {(₁, Y₁)}_₁ in counter-clockwise order. Use Green's theorem to show that P has area: 1 A = [(x1Y2 −X2Y1) + (X2Y3 − X3Y2) + ... + (Xn-1Yn — XnYn−1) + (XnY1 − X1Yn)]

Advanced Engineering Mathematics
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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Suppose that c is the line segment from (a, b) to (c,d). (a) Show that Briefly describe what this integral represents geometrically. Hint: Think back to linear algebra. What do determinants measure? (b) Suppose that a polygon P has vertices {(₁, y₁)} in counter-clockwise order. Use Green's theorem to show that P has area: A [zdy - ydr = ad-bc = [(X1Y2 − X2Y1) + (X2Y3 — T3Y2) + · ·· + (Xn-1Yn — TnYn-1) + (FnY1 − X1Yn)] - -
Transcribed Image Text:Suppose that c is the line segment from (a, b) to (c,d). (a) Show that Briefly describe what this integral represents geometrically. Hint: Think back to linear algebra. What do determinants measure? (b) Suppose that a polygon P has vertices {(₁, y₁)} in counter-clockwise order. Use Green's theorem to show that P has area: A [zdy - ydr = ad-bc = [(X1Y2 − X2Y1) + (X2Y3 — T3Y2) + · ·· + (Xn-1Yn — TnYn-1) + (FnY1 − X1Yn)] - -
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