Evaluate the line integral 7xy^4ds, where C is the right half of the circle x^2 + y^2 = 9.

Question

joachim · Answer

What are the steps I need to take to solve this problem?

irishboy123 · Answer

Find ds

Do you know how?

turingtest · Answer

I'm a bit rusty on line integrals, but it seems to be that it should be simple if we convert it to polar coordinates

joachim · Answer

I have started parametrizing x, y
$$x = 3\cos(t)$$
and
$$y = 3\sin(t)$$

turingtest · Answer

seems legit. 
what are the bounds on t?
what is ds?

joachim · Answer

I think t is bounded as follows:
$$\frac{ -\pi }{ 2 } \le t \le \frac{ \pi }{ 2 }$$

is that correct?

turingtest · Answer

I agree

joachim · Answer

I am unsure how I need to continue

turingtest · Answer

as IrishBoy said, you need ds
This is basically the arc length formula: do you know it?

joachim · Answer

ah of course, so I just calculate the arclenth and the integral is something like this?
$$17 \int\limits_{-\pi/2}^{\pi/2} 3\cos(t)(3\sin(t))^43dt$$

turingtest · Answer

yep :)

joachim · Answer

cool thanks for your help :)

turingtest · Answer

my pleasure!

joachim · Answer

constant should by 7