Evaluate the following iterated integrals. int_0^2int_0^1 4xy dx dy

Question
Integrals
Evaluate the following iterated integrals.
$$\int_0^2\int_0^1 4xy\ dx\ dy$$

2021-02-26
$$\text{Given integral}$$
$$\int_0^2\int_0^1 4xy\ dx\ dy$$
$$=\int_0^2 4[xdx]ydy$$
$$=\int_0^2 4\frac{x^2}{2}ydy$$
$$=\int_0^2 2[x^2]_0^1 ydy$$
$$=\int_0^2 2[1^2-0^2]ydy$$
$$=\int_0^2 2ydy$$
$$=2[\frac{y^2}{2}]_0^2$$
$$=[y^2]_0^2$$
$$=2^2-0^2$$
$$=4$$
$$\text{Therefore, the result of}\int_0^2\int_0^1 4xy\ dx\ dy\ is\ 4.$$

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