Question

In the problems of this section, set up and evaluate the integrals by hand and check your results by computer${\mathbf{\int }}_{\mathbf{x}\mathbf{=}\mathbf{1}}^{\mathbf{2}}{\mathbf{\int }}_{\mathbf{y}\mathbf{=}\mathbf{2}}^{\mathbf{1}}\mathbf{8}\mathbf{xy}\mathbf{}\mathbf{dxdy}\mathbf{.}$

Short answer

The required solution is -18

Step-by-step solution

Defining the Integrals

An integral is a mathematical notion that explains displacement, area, volume, and other ideas that come from the combination of infinitesimal data.

Integrating the problem

Consider the given information,

$$\begin{gathered} {\int }_{\mathrm{x}=1}^2{\int }_{y=-2}^{1}8\mathrm{xy}\mathrm{dxdy}=\left(4{\mathrm{x}}^2\overline{){}_1^2}\right)\left(\frac{1}{2}{\mathrm{y}}^2\overline{){}_{-2}^1}\right) \\ =-18 \end{gathered}$$

Therefore, the value is -18 .