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

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

Question
Integrals
asked 2021-02-25
Evaluate the following iterated integrals.
\(\int_0^2\int_0^1 4xy\ dx\ dy\)

Answers (1)

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

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