Solve int03 int12 x2y , dx , dy | Mathematics I 2079

Mathematics I20795 marksNumerical: double integralMultiple integrals

Solve $\int_0^3 \int_1^2 x^2y \, dx \, dy$ [5]

Solve $\int_0^3 \int_1^2 x^2y , dx , dy$ [5]

Integrand: $f(x,y) = x^2 y$ - Inner integral variable: $x$ , limits $[1, 2]$ - Outer integral variable: $y$ , limits $[0, 3]$ Treat $y$ as constant: $\int1^2 x^2 y \, dx = y \left[ \frac{x^3}{3} \right]1^2 = y\left(\frac{8}{3} - \frac{1}{3}\right) = \frac{7y}{3}$ $$\int0^3 \frac{7y}{3} , dy = ...

Integrand: $f(x,y) = x^2 y$ - Inner integral variable: $x$, limits $[1, 2]$ - Outer integral variable: $y$, limits $[0, 3]$ Treat $y$ as constant: $$\int1^2 x^2 y , dx = y \left[ \frac{x^3}{3} \right]1^2 = y\left(\frac{8}{3} - \frac{1}{3}\right) = \frac{7y}{3}$$ $$\int0^3 \frac{7y}{3} , dy = ...