Am I setting up my line integral correctly?

Asked Mar 30 '14 at 03:42

Active Mar 30 '14 at 04:04

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Evaluate the line integral

$$(x+xy+y) \, ds$$ where is the path of the arc along the circle given by $x^2+y^2=4$ starting at the point $(2,0)$ going counterclockwise making an inscribed angle of $\frac{3\pi}{4}$.

Started solving this problem by looking at the parametric equations $x = 2\cos t$ and $y=2\sin t$. I got the integral $4\cos t + 8\cos t \sin t + 4\sin t$ and I'm evaluating it from $0$ to $\frac{3\pi}{4}$. Am I doing this correctly?

edited Mar 30 '14 at 04:04

Mussé Redi

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asked Mar 30 '14 at 03:42

Ayoshna

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I think you should divide by $2$ the expression you're integrating. – Guest Mar 30 '14 at 03:46
Why do I need to divide it by 2? – Ayoshna Mar 30 '14 at 03:47
Because $x = 2 \cos(t)$ and $y = 2 \sin(t)$ and substituting in $x+xy+y$ gives $2 \cos(t) + 4 \cos(t) \sin(t) + 2 \sin(t)$. – Guest Mar 30 '14 at 03:48
Yes, but with line integral you have to multiply by the square root of the derivative of x plus the derivative of y. By doing that I got 2 so I multiplied it by 2. – Ayoshna Mar 30 '14 at 03:51
Right. Then it's ok. – Guest Mar 30 '14 at 03:51
I am integrating from 0 to 3(pi)/4 right? That was really the confusing part – Ayoshna Mar 30 '14 at 03:52
Yes doing this you will go counterclockwise making an inscribed angle of $\frac{3 \pi}{4}$. – Guest Mar 30 '14 at 03:54

Am I setting up my line integral correctly?

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