Question: "Evaluate the following iterated integrals. ∫02∫014xydxdy"

yogi55hr

Answered question

2021-11-08

Evaluate the following iterated integrals.

\int_{0}^{2} \int_{0}^{1} 4 x y d x d y

Xyle1991

Beginner2021-11-09Added 15 answers

Step 1
Given integral

\int_{0}^{2} \int_{0}^{1} 4 x y d x d y

= \int_{0}^{2} 4 [x d x] y d y

= \int_{0}^{2} 4 \frac{x^{2}}{2} y d y

= \int_{0}^{2} 2 {[x^{2}]}_{0}^{1} y d y

= \int_{0}^{2} 2 [1^{2} - 0^{2}] y d y

= \int_{0}^{2} 2 y d y

Step 2

= 2 {[\frac{y^{2}}{2}]}_{0}^{2}

= {[y^{2}]}_{0}^{2}

= 2^{2} - 0^{2}

=4
Therefore, the result of

\int_{0}^{2} \int_{0}^{1} 4 x y d x d y

is 4.

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