For the region R below, write ∫∫ZfdA as an integral in polar coordinates. Use t for θ in your expressions.

From the given figure, it is seen that the region R is bounded by two circles, x2+y2=9andx2+y2=16 Therefore, region R can be defined as R={(r,θ)3≤r≤4,0≤θ≤π} it is known that, ∫∫RfdA=∫θ1θ2f(rcos⁡θ,rsin⁡θ)rdrdθ Therefore, in polar co-ordinate, ∫∫RfdA=∫0π∫34f(rcos⁡θ,rsin⁡θ)rdrdθ (i) Thus, comparing (i) with ∫∫RfdA=∫0π∫34f(rcos⁡θ,rsin⁡θ)rdrdθ it is inferred that a = 0 b=π c = 3 d = 4 With dA=rdrdθ