Evaluate integral xy^4 ds

**Alpina540** · July 13th 2010, 11:23 AM

Evaluate the integral S xy^4 ds, where C is the right half of the circle x^2 +y^2=4

S= integral symbol

C= the lower bound of the integral

I am at a loss with this question, anyone know the answer?

Thanks

Possible answers
0.8
267.0
25.6
97.4
90.4

**Ackbeet** · July 13th 2010, 11:51 AM

I think your notation needs to be cleared up. Here's some LaTeX code for you. You can double-click to see how I did it:

$\int_{0}^{1}\frac{x}{x^{2}+4}\,dx.$

With that information, can you please re-post your problem?

**Alpina540** · July 13th 2010, 12:02 PM

Hows that I put the problem in a better format.

**HallsofIvy** · July 13th 2010, 12:44 PM

You need parametric equations. The simplest equations for a circle or radius R, center at (0, 0), are $x= R cos(\theta)$ and $y= R sin(\theta)$ where $\theta$ , the parameter, is the angle the positive x-axis makes with the radius to the point. Taking $\theta$ from $-\pi/2$ to $\pi/2$ will go from (0, -R) to (0, R), the semi-circle with x> 0.

Also $ds= \sqrt{\left(\frac{dx}{d\theta}\right)^2+ \left(\frac{dy}{d\theta}\right)^2}$ .

I suspect all that is in your text book very near this problem!

**Alpina540** · July 13th 2010, 12:49 PM

This is actually a worksheet that my Professor gave us but he didn't go over this type of problem very well in my view. The book has no examples of how to work these out either.

What would be the next steps?

Thanks Hall

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