Homework Sourser1 32sintheta r2 32sintheta I am supposed to find the area
r1 = 3-2sin(theta)
r2 = -3+2sin(theta)
I am supposed to find the area of the common region.
can someone tell me WHY integrating 1/2(r1)^2 from 0 to pi and then multiplying by 2 does not produce the same answer as integrating 1/2(r1)^2 from 0 to pi/2 and multiplying by 4?
thank you! quick question first good answer 5 stars. thanks!
fyi correct answer is 11pi - 24..
i keep getting 11pi + 24
r2 = -3+2sin(theta)
I am supposed to find the area of the common region.
can someone tell me WHY integrating 1/2(r1)^2 from 0 to pi and then multiplying by 2 does not produce the same answer as integrating 1/2(r1)^2 from 0 to pi/2 and multiplying by 4?
thank you! quick question first good answer 5 stars. thanks!
fyi correct answer is 11pi - 24..
i keep getting 11pi + 24
Solution
That is happening because the graph for r1 is not symmetric about the x-axis. (If you plot it, you\'ll see that the top half reaches (0, 2) and the bottom half (0, -4).) To find the area of the entire graph correctly, you could double the integral from = -/2 to /2. (The graph is symmetric on both-halves of the y-axis.)
