Answer
$m$ = $42k$
$\left(2,\frac{85}{28}\right)$
Work Step by Step
$m$ = $\int_1^3\int_1^4ky^2dydx$
$m$ = $\frac{1}{3}\int_1^3ky^3|_1^4dx$
$m$ = $\int_1^3{21k}dx$
$m$ = $21kx|_1^3$
$m$ = $42k$
$x̄$ = $\frac{1}{m}\int_1^3\int_1^4kxy^2dydx$
$x̄$ = $\frac{1}{42k}\int_1^3\int_1^4kxy^2dydx$
$x̄$ = $\frac{1}{42}\int_1^3{\frac{xy^3}{3}}|_1^4dx$
$x̄$ = $\frac{1}{42}\int_1^3{21x}dx$
$x̄$ = $\frac{1}{2}\int_1^3{x}dx$
$x̄$ = $\frac{1}{4}[x^2]|_1^3$
$x̄$ = $2$
$ȳ$ = $\frac{1}{m}\int_1^3\int_1^4ky^3dydx$
$ȳ$ = $\frac{1}{42k}\int_1^3\int_1^4ky^3dydx$
$ȳ$ = $\frac{1}{42}\int_1^3[\frac{y^4}{4}]_1^4dx$
$ȳ$ = $\frac{1}{42}\int_1^3{\frac{255}{4}}dx$
$ȳ$ = $\frac{255}{168}[x]_1^3$
$ȳ$ = $\frac{85}{28}$
