## Thomas' Calculus 13th Edition

2 $ln$ 2
We solve the double integral as follows: $\int\int_R\frac{xy^3}{s^2+1}dA$ =$\int_{0}^{1}\int^{2}_{0}\frac{xy^3}{s^2+1}dy dx$ =$\int^{1}_{0}[\frac{xy^4}{4(s^2+1)}]_0^2$ =$\int^{1}_{0}\frac{4x}{x^2+1}dx$ =$[2 ln|x^2+1|]^1_0$ =2 $ln$ 2