1. Evaluate the integral ſ F. dr where C is given by the vector function r(t) a) F(x,y) = xyi + 3y²j_r(t)=11t¹i+t³j 0≤t≤1 b) F(x,y,z) = (x+y)i + (y-z)j +z²k_r(t) = t²i+t³j+t²k 0≤t≤1 c) F(x,y,z) = sin(x)i + cos(y)j +xzk_r(t) = t³i- t²j+ tk 0≤t≤1

1. Evaluate the integral ſ F. dr where C is given by the vector function r(t) a) F(x,y) = xyi + 3y²j_r(t)=11t¹i+t³j 0≤t≤1 b) F(x,y,z) = (x+y)i + (y-z)j +z²k_r(t) = t²i+t³j+t²k 0≤t≤1 c) F(x,y,z) = sin(x)i + cos(y)j +xzk_r(t) = t³i- t²j+ tk 0≤t≤1

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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Question

show full and complete procedure HANDWRITTEN ONLY please answer parts a), b) & c) as they are subparts of the same question

1. Evaluate the integral ſ F. dr where C is given by the vector function r(t)
a) F(x,y) = xyi + 3y²j_r(t)=11t¹i+t³j
0≤t≤1
b) F(x,y,z) = (x+y)i + (y-z)j +z²k_r(t) = t²i+t³j+t²k 0≤t≤1
c) F(x,y,z) = sin(x)i + cos(y)j +xzk_r(t) = t³i- t²j+ tk 0≤t≤1

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