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(Solved): Suppose C is the curve r(t)=(:2t,2t^(3):), for 0<=t<=4, and F=(:3x,3y:). Evaluate \int_C F*Tds ...



Suppose

C

is the curve

r(t)=(:2t,2t^(3):)

, for

0<=t<=4

, and

F=(:3x,3y:)

. Evaluate

\int_C F*Tds

using the following steps. a. Convert the line integral

\int_C F*Tds

to an ordinary integral. b. Evaluate the integral in part (a). a. Convert the line integral

\int_C F*Tds

to an ordinary integral.

\int_C F*Tds=\int_0 dt (Simplify your answers.)

The value of the line integral of

F

over

C

is

(Type an exact answer, using radicals as needed.)



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