Undeuxtroiscatsank?
New member
- Joined
- Oct 28, 2007
- Messages
- 3
Hi, I was wondering if someone can help me complete this multi-step problem. The parts I've done are in blue. I'll post the whole of it, first (sorry, I don't know how to post an image of the curve):
The curve above is drawn in the xy-plane and is described by the equation in polar coordinates r = ? + sin(2 ?) for 0 ? ? ? ?, where r is measured in meters and ? is measured in radians. The derivative of r with respect to ? is given by dr/d? = 1 + 2cos(2?).
a) find the area bounded by the curve and the x-axis.
So, for this, the area formula would be 1/2 ? r^2 d?, no? So it would end up being:
1/2 ?( ? + sin(2 ?) )^2
But what would be the limits of integration? How could you find them without using the graph?
b) find the angle ? that corresponds to the point on the curve with x-coordinate -2.
?
I thik it means that since x = r cos ? = f(?) cos ? , you get this:
-2 = (? + sin(2 ?)) cos ?
Is this right? Am I just supposed to solve for??
c) For ?/3 < ? < 2?/3, dr/d? is negative. What does this fact say about r? What does this fact say about the curve?
I don't know. An explanation would be much appreciated.
d) Find the value of ? in the interval 0 ? ? ? ?/2 that corresponds to the point on the curve in the first quadrant with greatest distance from the origin. Justify your answer.
? Same as part c.
I'd really appreciate any help you can offer. Thank you again!
The curve above is drawn in the xy-plane and is described by the equation in polar coordinates r = ? + sin(2 ?) for 0 ? ? ? ?, where r is measured in meters and ? is measured in radians. The derivative of r with respect to ? is given by dr/d? = 1 + 2cos(2?).
a) find the area bounded by the curve and the x-axis.
So, for this, the area formula would be 1/2 ? r^2 d?, no? So it would end up being:
1/2 ?( ? + sin(2 ?) )^2
But what would be the limits of integration? How could you find them without using the graph?
b) find the angle ? that corresponds to the point on the curve with x-coordinate -2.
?
I thik it means that since x = r cos ? = f(?) cos ? , you get this:
-2 = (? + sin(2 ?)) cos ?
Is this right? Am I just supposed to solve for??
c) For ?/3 < ? < 2?/3, dr/d? is negative. What does this fact say about r? What does this fact say about the curve?
I don't know. An explanation would be much appreciated.
d) Find the value of ? in the interval 0 ? ? ? ?/2 that corresponds to the point on the curve in the first quadrant with greatest distance from the origin. Justify your answer.
? Same as part c.
I'd really appreciate any help you can offer. Thank you again!