Evaluate the line integral, where C is the given curve. int_C xy ds, C:x = t^2,y = 2t, 0 <= t <= 3

Scarlet Marshall

Scarlet Marshall

Answered question

2022-11-24

Evaluate the line integral, where C is the given curve.
C x y d s , C : x = t 2 , y = 2 t , 0 t 3
thanks show all work and steps

Answer & Explanation

SquingonottokQqk

SquingonottokQqk

Beginner2022-11-25Added 8 answers

Evaluate the line integral, where C is the given curve.
C x y d s , C : x = t 2 , y = 2 t , 0 t 3
x = 2 t y = 2
d s = ( x 2 ) + ( y 2 ) = 4 t 2 + 4 C x y d s = 0 3 t 2 .2 t .2 . 1 + t 2 d t = 0 3 4 t 3 1 + t 2 d t
t = t a n θ d t = ( 1 + t a n 2 θ ) d θ = ( s e c 2 θ ) d θ
= 0 3 4 t 3 1 + t 2 d t = 8 15 ( 1 + 125. 10 )

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