What is the area enclosed by #r=theta^2cos(theta+pi/4)-sin(2theta-pi/12) # for #theta in [pi/12,pi]#?
The area is about 19.1849 by computational integration.
cited from a Japanese site, 極座標表示の場合の面積 http://www.geocities.jp/phaosmath/int1/polar.htm
Thus, the area in this question is:
This integration is so hard…
According to www.wolframalpha.com