Get the answer to "Evaluate the line integral along the path C..."

Barbara Schroder

Answered question

2021-11-15

Evaluate the line integral along the path C given by

x = 2 t, y = 10 t,

where

0 \leq t \leq 1 \int c x y d x + y d y

Momp1989

Beginner2021-11-16Added 21 answers

\int_{C} x y d x + y d y

Given that

x = 2 t

and

y = 4 t

Therefore,

d x = 2 d t

and

d y = 4 d t

Substitute the value to get

\int_{C} (2 t \times 4 t) (2 d t) + (4 t) (4 d t)

Given that

0 \leq t \leq 1

, therefore we will integrate from 0 to 1

\int_{0}^{1} 16 t^{2} + 16 t d t = {[\frac{16 t^{3}}{3} + \frac{16 t^{2}}{2}]}_{0}^{1}

= {[\frac{16 t^{}}{3} + 8 t^{2}]}_{0}^{1}

= \frac{16}{3} + 8

= \frac{16 + 24}{3}

= \frac{40}{3}

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