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Suppose the planar region R lies in the rectangle a

Suppose the planar region R lies in the rectangle a

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 the planar region R lies in the rectangle a <r< b c<y< d. (Note: R is not the whole rectangle.) Show that the centroid (T, 9) of R also lies in the rectangle. Hint: write down an expression for 7. What can you say about the denominator? Can you find bounds for the numerator? What are you trying to show anyway? Formulas: SSf(x, y, z)dS = SS f(x,y, z); ||Vh|| dA |Vh . k| S D SSF · ndS = SS F. Vh -dA %3D |Vh · k| D Area (cylinder)=2rrh Volume (Cylinder)=rr²h Area (Sphere)=4rr² Volume (Sphere)=Tr³ Theorems: fF dT = S[s(VxF)· nds Jend flbeg SVf •dF de' -)dA dy ӘР SPdx + Qdy = SSp(
Transcribed Image Text:Suppose the planar region R lies in the rectangle a <r< b c<y< d. (Note: R is not the whole rectangle.) Show that the centroid (T, 9) of R also lies in the rectangle. Hint: write down an expression for 7. What can you say about the denominator? Can you find bounds for the numerator? What are you trying to show anyway? Formulas: SSf(x, y, z)dS = SS f(x,y, z); ||Vh|| dA |Vh . k| S D SSF · ndS = SS F. Vh -dA %3D |Vh · k| D Area (cylinder)=2rrh Volume (Cylinder)=rr²h Area (Sphere)=4rr² Volume (Sphere)=Tr³ Theorems: fF dT = S[s(VxF)· nds Jend flbeg SVf •dF de' -)dA dy ӘР SPdx + Qdy = SSp(
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