Question

Use a double integral in polar coordinates to find the area taken up by one petal of the rose
curve r = sin 2θ .

Please explain step by step

Answer 1

very nice one lad! first we want to draw this region. then we will see that our integration boundaries should be 0<theta<pi/2 and r is between 0 and sin2theta. thus it would be set up as double integral(sin2theta)rdr dtheta. i rather sure this is how to do it. what ya think?

Answer 2

check this out! http://tutorial.math.lamar.edu/Classes/CalcIII/DIPolarCoords.aspx theres basically an exact example!

Answer 3

@.Sam. what is that graph?
looks like r=theta

Answer 4

That seems to be a logarithmic spiral: \[r = e^\theta\]

Answer 5

(p.s. referring to sam)