1. The problem statement, all variables and given/known data Find the area enclosed by the polar curve r = 2 e^(0.9theta) on the interval 0 <= theta <= 1/8 and the straight line segment between its ends. 2. Relevant equations arclength = 3. The attempt at a solution I need help finding the boundaries for this problem. Is it from 0 to pi? I'm not sure how exactly would I go about finding the limits of integration(boundaries) since it starts from the origin and ends at the x-axis.
The integration boundaries for theta are given. [Hint: first find the area between the curve and the x-axis, then find the area under the straight line segment between its ends and subtract appropriately.]
Yes. Note that the dtheta is outside the square root and don't forget the Jacobian factor when doing an integral in polar coordinates.
i thought it meant arclength, but i guess it is area so it should be int [a->b] of (1/2(r)^2)dtheta but I still don't know how to set up this problem correctly