# Thread: solving line integral by bounded area

1. ## solving line integral by bounded area

calculate $\int_{c}Fdr where F(x,y)=(e^{x}-4ycos^{2}x)i+(2x-sin2x-ln(y^{2}+1))j$ and the curve C is $y(x)=-\sqrt{1-x^{2}}$ where $-1\leq x\leq1$

i closed this curve with y=0 and did double integral over the bounded area
instead of caulculating the curve integral.

in the photo it written that it wrong i dont know why?

2. ## Re: solving line integral by bounded area

Originally Posted by transgalactic
in the photo it written that it wrong i dont know why?

Would you read a document presented in this way?

flipped it.
is it ok ?

4. ## Re: solving line integral by bounded area

Your error is not completing the boundary- the integral around the semi-circle is equal to the integral over the area minus the integral along the x-axis.

But the obvious way to do it is directly- use parametric equations: $x= cos(\theta)$, '$y= sin(\theta)$, $dx= -sin(\theta)d\theta$, $dy= cos(\theta)d\theta$, $\theta$ from $\pi$ to $2\pi$ (assuming you are integrating from (-1, 0) to (1, 0), you don't mention the orientation).

thanks