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Help converting integral from coordinate to polar?
coordinate: ∫∫sin(x2+y2)dA over the region 16<=x^2+y^2<=64
convert to polar coordinates and solve.
I think the integrand should be rsin(r^2)drdtheta, but I'm stuck on the limits of integration...help?
2 Answers
- ?Lv 71 decade agoFavorite Answer
x^2 + y^2 = r^2
Integrand becomes r sin r^2 dr dw (where w = angle)
16 < r^2 < 64 is the same as 4 < r < 8
Limits of integration with respect to r are 4 to 8
Limits of integratation with respect to w are 0 to 2pi
- ?Lv 44 years ago
the 1st answer is incredibly superb suitable, diverse than that the portion of integration is a one million/2-circle (that component of the circle x² + y² = a² to the superb suitable of the y-axis), so the shrink decrease back on ? would desire to be -?/2. it is going to be the quarter-circle indicated if the barriers on y have been 0 to a.
